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Projective Curvature Tensor of Riemannian Manifolds Admitting A Projective Semi-Symmetric Connection

Yıl 2020, , 78 - 85, 22.06.2020

S. K. Chaubey Pankaj R. B. Kanaujia S. K. Yadav

https://doi.org/10.32323/ujma.650209
Cited By: 2

Öz

The aim of the present paper is to study the properties of Riemannian manifolds equipped with a projective semi-symmetric connection.

Anahtar Kelimeler

Riemannian manifolds Projective semi-symmetric connection Different curvature tensors nullity distribution quasi Einstein manifolds

Kaynakça

  • [1] A. A. Shaikh, Young Ho Kim and S. K. Hui, On Lorentzian quasi-Einstein manifolds, J. Korean Math. Soc., Vol. 48 (4), (2011), 669-689.
  • [2] A. Friedmann and J. A. Schouten, ¨U ber die geometrie der halbsymmetrischen ¨ ubertragung, Math. Zeitschr, 21, (1924), pp. 211-223.
  • [3] A. Kumar and S. K. Chaubey, A semi-symmetric non-metric connection in a generalized co-symplectic manifold, Int. Journal of Math. Analysis, 4(17), (2010), 809-817.
  • [4] A. K. Dubey, S. K. Chaubey and R. H. Ojha, On semi-symmetric non-metric connection, International Mathematical Forum, 5 (15), (2010), 731-737.
  • [5] A. Sharfuddin and S. I. Husain, Semi-symmetric metric connections in almost contact manifolds, Tensor N. S., 30 (1976), 133-139.
  • [6] B. O’ Neill, Semi-Riemannian Geometry with Applications to the Relativity, Academic Press, New York- London, 1983.
  • [7] D. E. Blair, Contact manifolds in Riemannian Geometry, Lecture Notes in Mathematics, Vol. 509, Springer-Verlag, Berlin, 1976.
  • [8] ´E . Cartan, Sur une classe remarquable d’espaces de Riemannian, Bull. Soc. Math. France, 54 (1926), 214-264.
  • [9] ´E . Cartan, Le cons sur la geometrie des espaces de Riemann, 2nd ed., Paris, 1946.
  • [10] H. A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc., 34, (1932), pp. 27-50.
  • [11] H. Stephani, General relativity-An introduction to the theory of gravitational field, Cambridge Univ. Press, Cambridge, 1982.
  • [12] J. V. Narlikar, General relativity and gravitation, The Macmillan co. of India, 1978.
  • [13] K. Yano, On semi-symmetric metric connection, Rev. Roumaine de Math. Pures et Appl., 15 (1970), 1579-1586.
  • [14] M. C. Chaki and R. K. Maithy, On quasi Einstein manifolds, Publ. Math. Debrecen, 57, no. 3-4 (2000), 297-306.
  • [15] M. Okumura, Some remarks on space with a certain contact structure, Tohoku Math. J., 14 (1962), 135-145.
  • [16] M. C. Chaki, On generalized quasi Einstein manifolds, Publ. Math. Debrecen, 58, 4 (2001), 683-691.
  • [17] M. M. Tripathi and J. S. Kim, On N(k)-quasi Einstein manifolds, Commun. Korean Math. Soc., 22, no. 3 (2007), 411-417.
  • [18] N. S. Agashe and M. R. Chafle, A semi-symmetric non-metric connection in a Riemannian manifold, Indian J. Pure Appl. Math., 23 (1992), 399-409.
  • [19] O. Bahadır and S. K. Chaubey, Some notes on LP-Sasakian Manifolds with Generalized Symmetric Metric Connection, Honam Mathematical Journal (2020) (Accepted) arXiv:1805.00810v2 [math.DG] 17 Oct 2019.
  • [20] P. Alegre, David E. Blair and A. Carriazo, Generalized Sasakian Space forms, Israel J. of Math, 141 (2004), 157-183.
  • [21] P. Zhao and H. Song, An invariant of the projective semi-symmetric connection, Chinese Quarterly J. of Math., 16 (4), (2001), 48-52.
  • [22] P. Zhao, Some properties of projective semi-symmetric connection, Int. Math. Forum, 3(7), (2008), 341-347.
  • [23] P. Debnath and A. Konar, On quasi Einstein manifold and quasi Einstein spacetime, Differential Geometry-Dynamical Systems, 12 (2010), 73-82.
  • [24] Pankaj, S. K. Chaubey and R. Prasad, Trans-Sasakian Manifolds with respect to a non-symmetric non-metric connection, Global Journal of Advanced Research on Classical and Modern Geometries, Vol.7, (2018), Issue 1, 1-10.
  • [25] R. N. Singh, S. K. Pandey and Giteshwari Pandey, On semi-symmetric metric connection in an SP-Sasakian manifold, Proc. of the Nat. Academy of Sci., 83 (1) (2013), 39-47.
  • [26] R. Prasad and Pankaj, Some curvature tensors on a trans-Sasakian manifold with respect to semi symmetric non-metric connection, J. Nat. Acad. Math, Sp. Volume (2009), 55-64.
  • [27] R. S. Mishra and S. N. Pandey, Semi-symmetric metric connections in an almost contact manifold, Indian J. Pure Appl. Math., 9, No. 6 (1978), 570-580.
  • [28] S. Guha, On quasi Einstein and generalized quasi Einstein manifolds, Facta Univ. Ser. Mech. Automat. Control Robot, 3, 14 (2003), 821-842.
  • [29] S. K. Pal, M. K. Pandey and R. N. Singh, On a type of projective semi-symmetric connection, Int. J. of Anal. and Appl., 7(2) (2015), 153-161.
  • [30] S. K. Chaubey and A. Kumar, Semi-symmetric metric T-connection in an almost contact metric manifold, International Mathematical Forum, 5, (2010), no. 23, 1121 - 1129.
  • [31] S. K. Chaubey and R. H. Ojha, On a semi-symmetric non-metric and quarter-symmetric metric connections, Tensor N. S., 70 (2), (2008), 202-213.
  • [32] S. K. Chaubey and R. H. Ojha, On a semi-symmetric non-metric connection, Filomat, 26 (2), (2012), 269-275.
  • [33] S. K. Chaubey, Almost contact metric manifolds admitting semi-symmetric non-metric connection, Bulletin of Mathematical Analysis and Applications, 3(2), (2011), 252-260.
  • [34] S. K. Chaubey and A. C. Pandey, Some Properties of a Semi-symmetric Non-metric Connection on a Sasakian Manifold, Int. J. Contemp. Math. Sciences, 8(16) (2013), 789-799.
  • [35] S. K. Chaubey, Existence of N(k)-quasi Einstein manifolds, Facta Universitatis (NIS) Ser. Math. Inform., 32 (3), (2017), 369-385.
  • [36] S. K. Chaubey and S. K. Yadav, Study of Kenmotsu manifolds with semi-symmetric metric connection, Universal Journal of Mathematics and Applications, 1 (2) (2018), 89-97.
  • [37] S. K. Chaubey and U. C. De, Characterization of the Lorentzian para-Sasakian manifolds admitting a quarter-symmetric non-metric connection, SUT Journal of Mathematics, 55 (1), (2019), 53-67.
  • [38] S. K. Chaubey and A. Yildiz, Riemannian manifolds admitting a new type of semi symmetric nonmetric connection, Turk. J. Math., 43, (2019), 1887-1904.
  • [39] S. K. Chaubey and U. C. De, Lorentzian para-Sasakian manifolds admitting a new type of quarter symmetric non-metric x -connection, International Electronic Journal of Geometry, 12 (2), (2019), 266-275.
  • [40] S. K. Chaubey, J. W. Lee and S. Yadav, Riemannian manifolds with a semi-symmetric metric Pconnection J. Korean Math. Soc., 56 (4), (2019), 1113-1129.
  • [41] S. Tanno, Ricci curvatures of contact Riemannian manifolds, Tohoku Math. J., 40 (1988), 441-417.
  • [42] S. Yadav, S. K. Chaubey and R. Prasad, On Kenmotsu manifolds with a semi-symmetric metric connection, Facta Universitatis (NIS) Ser. Math. Inform., Vol. 35, No.-1 (2020), 101-119.
  • [43] T. Imai, Notes on semi-symmetric metric connections, Tensor N. S., 24 (1972), 293-296.
  • [44] T. Takahashi, Sasakian f-symmetric spaces, Tohoku Math. J., 29 (1977), 91–113.
  • [45] U. C. De and B. K. De, On Quasi Einstein Manifolds, Commun. Korean Math. Soc. 23 (2008), No. 3, pp. 413–420.
  • [46] U. C. De and G. C. Ghosh, On quasi Einstein and special quasi Einstein manifolds, Proc. of the Int. conf. of Mathematics and its applications, Kuwait University, April 5-7, (2004), 178-191.
  • [47] U. C. De and G. C. Ghosh, On quasi Einstein manifolds, Period. Math. Hungar., 48, (1-2) (2004), 223-231.
  • [48] U. C. De and J. Sengupta, On a type of semi-symmetric metric connection on an almost contact metric manifold, Filomat, 14 (2000), 33-42.
  • [49] Z. I. Szabo, Structure theorems on Riemannian spaces satisfying R(X;Y)R = 0 I, The local version, J. Differ. Geometry 17 (1982), 531-582.
  • [50] Z. I. Szabo, Structure theorems on Riemannian spaces satisfying R(X;Y)R = 0 II, Global version, Geom. Dedicata 19 (1985), 65-108.

Yıl 2020, , 78 - 85, 22.06.2020

S. K. Chaubey Pankaj R. B. Kanaujia S. K. Yadav

https://doi.org/10.32323/ujma.650209
Cited By: 2

Öz

Kaynakça

  • [1] A. A. Shaikh, Young Ho Kim and S. K. Hui, On Lorentzian quasi-Einstein manifolds, J. Korean Math. Soc., Vol. 48 (4), (2011), 669-689.
  • [2] A. Friedmann and J. A. Schouten, ¨U ber die geometrie der halbsymmetrischen ¨ ubertragung, Math. Zeitschr, 21, (1924), pp. 211-223.
  • [3] A. Kumar and S. K. Chaubey, A semi-symmetric non-metric connection in a generalized co-symplectic manifold, Int. Journal of Math. Analysis, 4(17), (2010), 809-817.
  • [4] A. K. Dubey, S. K. Chaubey and R. H. Ojha, On semi-symmetric non-metric connection, International Mathematical Forum, 5 (15), (2010), 731-737.
  • [5] A. Sharfuddin and S. I. Husain, Semi-symmetric metric connections in almost contact manifolds, Tensor N. S., 30 (1976), 133-139.
  • [6] B. O’ Neill, Semi-Riemannian Geometry with Applications to the Relativity, Academic Press, New York- London, 1983.
  • [7] D. E. Blair, Contact manifolds in Riemannian Geometry, Lecture Notes in Mathematics, Vol. 509, Springer-Verlag, Berlin, 1976.
  • [8] ´E . Cartan, Sur une classe remarquable d’espaces de Riemannian, Bull. Soc. Math. France, 54 (1926), 214-264.
  • [9] ´E . Cartan, Le cons sur la geometrie des espaces de Riemann, 2nd ed., Paris, 1946.
  • [10] H. A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc., 34, (1932), pp. 27-50.
  • [11] H. Stephani, General relativity-An introduction to the theory of gravitational field, Cambridge Univ. Press, Cambridge, 1982.
  • [12] J. V. Narlikar, General relativity and gravitation, The Macmillan co. of India, 1978.
  • [13] K. Yano, On semi-symmetric metric connection, Rev. Roumaine de Math. Pures et Appl., 15 (1970), 1579-1586.
  • [14] M. C. Chaki and R. K. Maithy, On quasi Einstein manifolds, Publ. Math. Debrecen, 57, no. 3-4 (2000), 297-306.
  • [15] M. Okumura, Some remarks on space with a certain contact structure, Tohoku Math. J., 14 (1962), 135-145.
  • [16] M. C. Chaki, On generalized quasi Einstein manifolds, Publ. Math. Debrecen, 58, 4 (2001), 683-691.
  • [17] M. M. Tripathi and J. S. Kim, On N(k)-quasi Einstein manifolds, Commun. Korean Math. Soc., 22, no. 3 (2007), 411-417.
  • [18] N. S. Agashe and M. R. Chafle, A semi-symmetric non-metric connection in a Riemannian manifold, Indian J. Pure Appl. Math., 23 (1992), 399-409.
  • [19] O. Bahadır and S. K. Chaubey, Some notes on LP-Sasakian Manifolds with Generalized Symmetric Metric Connection, Honam Mathematical Journal (2020) (Accepted) arXiv:1805.00810v2 [math.DG] 17 Oct 2019.
  • [20] P. Alegre, David E. Blair and A. Carriazo, Generalized Sasakian Space forms, Israel J. of Math, 141 (2004), 157-183.
  • [21] P. Zhao and H. Song, An invariant of the projective semi-symmetric connection, Chinese Quarterly J. of Math., 16 (4), (2001), 48-52.
  • [22] P. Zhao, Some properties of projective semi-symmetric connection, Int. Math. Forum, 3(7), (2008), 341-347.
  • [23] P. Debnath and A. Konar, On quasi Einstein manifold and quasi Einstein spacetime, Differential Geometry-Dynamical Systems, 12 (2010), 73-82.
  • [24] Pankaj, S. K. Chaubey and R. Prasad, Trans-Sasakian Manifolds with respect to a non-symmetric non-metric connection, Global Journal of Advanced Research on Classical and Modern Geometries, Vol.7, (2018), Issue 1, 1-10.
  • [25] R. N. Singh, S. K. Pandey and Giteshwari Pandey, On semi-symmetric metric connection in an SP-Sasakian manifold, Proc. of the Nat. Academy of Sci., 83 (1) (2013), 39-47.
  • [26] R. Prasad and Pankaj, Some curvature tensors on a trans-Sasakian manifold with respect to semi symmetric non-metric connection, J. Nat. Acad. Math, Sp. Volume (2009), 55-64.
  • [27] R. S. Mishra and S. N. Pandey, Semi-symmetric metric connections in an almost contact manifold, Indian J. Pure Appl. Math., 9, No. 6 (1978), 570-580.
  • [28] S. Guha, On quasi Einstein and generalized quasi Einstein manifolds, Facta Univ. Ser. Mech. Automat. Control Robot, 3, 14 (2003), 821-842.
  • [29] S. K. Pal, M. K. Pandey and R. N. Singh, On a type of projective semi-symmetric connection, Int. J. of Anal. and Appl., 7(2) (2015), 153-161.
  • [30] S. K. Chaubey and A. Kumar, Semi-symmetric metric T-connection in an almost contact metric manifold, International Mathematical Forum, 5, (2010), no. 23, 1121 - 1129.
  • [31] S. K. Chaubey and R. H. Ojha, On a semi-symmetric non-metric and quarter-symmetric metric connections, Tensor N. S., 70 (2), (2008), 202-213.
  • [32] S. K. Chaubey and R. H. Ojha, On a semi-symmetric non-metric connection, Filomat, 26 (2), (2012), 269-275.
  • [33] S. K. Chaubey, Almost contact metric manifolds admitting semi-symmetric non-metric connection, Bulletin of Mathematical Analysis and Applications, 3(2), (2011), 252-260.
  • [34] S. K. Chaubey and A. C. Pandey, Some Properties of a Semi-symmetric Non-metric Connection on a Sasakian Manifold, Int. J. Contemp. Math. Sciences, 8(16) (2013), 789-799.
  • [35] S. K. Chaubey, Existence of N(k)-quasi Einstein manifolds, Facta Universitatis (NIS) Ser. Math. Inform., 32 (3), (2017), 369-385.
  • [36] S. K. Chaubey and S. K. Yadav, Study of Kenmotsu manifolds with semi-symmetric metric connection, Universal Journal of Mathematics and Applications, 1 (2) (2018), 89-97.
  • [37] S. K. Chaubey and U. C. De, Characterization of the Lorentzian para-Sasakian manifolds admitting a quarter-symmetric non-metric connection, SUT Journal of Mathematics, 55 (1), (2019), 53-67.
  • [38] S. K. Chaubey and A. Yildiz, Riemannian manifolds admitting a new type of semi symmetric nonmetric connection, Turk. J. Math., 43, (2019), 1887-1904.
  • [39] S. K. Chaubey and U. C. De, Lorentzian para-Sasakian manifolds admitting a new type of quarter symmetric non-metric x -connection, International Electronic Journal of Geometry, 12 (2), (2019), 266-275.
  • [40] S. K. Chaubey, J. W. Lee and S. Yadav, Riemannian manifolds with a semi-symmetric metric Pconnection J. Korean Math. Soc., 56 (4), (2019), 1113-1129.
  • [41] S. Tanno, Ricci curvatures of contact Riemannian manifolds, Tohoku Math. J., 40 (1988), 441-417.
  • [42] S. Yadav, S. K. Chaubey and R. Prasad, On Kenmotsu manifolds with a semi-symmetric metric connection, Facta Universitatis (NIS) Ser. Math. Inform., Vol. 35, No.-1 (2020), 101-119.
  • [43] T. Imai, Notes on semi-symmetric metric connections, Tensor N. S., 24 (1972), 293-296.
  • [44] T. Takahashi, Sasakian f-symmetric spaces, Tohoku Math. J., 29 (1977), 91–113.
  • [45] U. C. De and B. K. De, On Quasi Einstein Manifolds, Commun. Korean Math. Soc. 23 (2008), No. 3, pp. 413–420.
  • [46] U. C. De and G. C. Ghosh, On quasi Einstein and special quasi Einstein manifolds, Proc. of the Int. conf. of Mathematics and its applications, Kuwait University, April 5-7, (2004), 178-191.
  • [47] U. C. De and G. C. Ghosh, On quasi Einstein manifolds, Period. Math. Hungar., 48, (1-2) (2004), 223-231.
  • [48] U. C. De and J. Sengupta, On a type of semi-symmetric metric connection on an almost contact metric manifold, Filomat, 14 (2000), 33-42.
  • [49] Z. I. Szabo, Structure theorems on Riemannian spaces satisfying R(X;Y)R = 0 I, The local version, J. Differ. Geometry 17 (1982), 531-582.
  • [50] Z. I. Szabo, Structure theorems on Riemannian spaces satisfying R(X;Y)R = 0 II, Global version, Geom. Dedicata 19 (1985), 65-108.
Toplam 50 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

S. K. Chaubey 0000-0002-3882-4596

Pankaj R. B. Kanaujia 0000-0002-3313-6006

S. K. Yadav

Yayımlanma Tarihi 22 Haziran 2020
Gönderilme Tarihi 23 Kasım 2019
Kabul Tarihi 14 Nisan 2020
Yayımlandığı Sayı Yıl 2020

Kaynak Göster

APA Chaubey, S. K., R. B. Kanaujia, P., & Yadav, S. K. (2020). Projective Curvature Tensor of Riemannian Manifolds Admitting A Projective Semi-Symmetric Connection. Universal Journal of Mathematics and Applications, 3(2), 78-85. https://doi.org/10.32323/ujma.650209
AMA Chaubey SK, R. B. Kanaujia P, Yadav SK. Projective Curvature Tensor of Riemannian Manifolds Admitting A Projective Semi-Symmetric Connection. Univ. J. Math. Appl. Haziran 2020;3(2):78-85. doi:10.32323/ujma.650209
Chicago Chaubey, S. K., Pankaj R. B. Kanaujia, ve S. K. Yadav. “Projective Curvature Tensor of Riemannian Manifolds Admitting A Projective Semi-Symmetric Connection”. Universal Journal of Mathematics and Applications 3, sy. 2 (Haziran 2020): 78-85. https://doi.org/10.32323/ujma.650209.
EndNote Chaubey SK, R. B. Kanaujia P, Yadav SK (01 Haziran 2020) Projective Curvature Tensor of Riemannian Manifolds Admitting A Projective Semi-Symmetric Connection. Universal Journal of Mathematics and Applications 3 2 78–85.
IEEE S. K. Chaubey, P. R. B. Kanaujia, ve S. K. Yadav, “Projective Curvature Tensor of Riemannian Manifolds Admitting A Projective Semi-Symmetric Connection”, Univ. J. Math. Appl., c. 3, sy. 2, ss. 78–85, 2020, doi: 10.32323/ujma.650209.
ISNAD Chaubey, S. K. vd. “Projective Curvature Tensor of Riemannian Manifolds Admitting A Projective Semi-Symmetric Connection”. Universal Journal of Mathematics and Applications 3/2 (Haziran 2020), 78-85. https://doi.org/10.32323/ujma.650209.
JAMA Chaubey SK, R. B. Kanaujia P, Yadav SK. Projective Curvature Tensor of Riemannian Manifolds Admitting A Projective Semi-Symmetric Connection. Univ. J. Math. Appl. 2020;3:78–85.
MLA Chaubey, S. K. vd. “Projective Curvature Tensor of Riemannian Manifolds Admitting A Projective Semi-Symmetric Connection”. Universal Journal of Mathematics and Applications, c. 3, sy. 2, 2020, ss. 78-85, doi:10.32323/ujma.650209.
Vancouver Chaubey SK, R. B. Kanaujia P, Yadav SK. Projective Curvature Tensor of Riemannian Manifolds Admitting A Projective Semi-Symmetric Connection. Univ. J. Math. Appl. 2020;3(2):78-85.

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