Research Article
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Year 2018, , 89 - 97, 26.06.2018
https://doi.org/10.32323/ujma.427238

Abstract

References

  • [1] Robert Osserman, Curvature in the Eighties, The American mathematical monthly 97 (8), (1990), 731-756.
  • [2] ´E . Cartan, Surune classe remarquable d’espaces de Riemannian, Bull. Soc. Math. France 54 (1926), 214- 264.
  • [3] ´E . Cartan, Le cons sur la g ´eeom´ etrie des espaces de Riemann, 2nd ed., Paris, 1946.
  • [4] B. O’ Neill, Semi-Riemannian geometry with applications to the relativity, Academic Press, New York- London, 1983.
  • [5] M. M. Boothby and R. C. Wong, On contact manifolds, Anna. Math. 68 (1958), 421-450.
  • [6] S. Sasaki and Y. Hatakeyama, On differentiable manifolds with certain structures which are closely related to almost contact structure, Tohoku Math. J. 13 (1961), 281-294.
  • [7] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24 (1972), 93-103.
  • [8] S. K. Chaubey and A. A. Shaikh, On 3-dimensional Lorentzian concircular structure manifolds, Commun. Korean Math. Soc., 33 (2018) https://doi.org/10.4134/CKMS.c180044.
  • [9] S. K. Chaubey and R. H. Ojha, On the m-projective curvature tensor of a Kenmotsu manifold, Differential Geometry - Dynamical Systems 12 (2010), 52-60.
  • [10] S. K. Chaubey, S. Prakash and R. Nivas, Some properties of m􀀀projective curvature tensor in Kenmotsu manifolds, Bulletin of Math Analysis and Applications 4 (2012), 48-56.
  • [11] S. K. Chaubey and C. S. Prasad, On generalized f􀀀recurrent Kenmotsu manifolds, TWMS J. App. Eng. Math. 5 (1) (2015), 1-9.
  • [12] S. K. Yadav, S. K. Chaubey and D. L. Suthar, Certain results on almost Kenmotsu (k;m;n)􀀀spaces, Konuralp Journal of Mathematics 6 (1) (2018) 128-133.
  • [13] S. K. Chaubey, A. C. Pandey, N. V. C. Shukla, Some properties of Kenmotsu manifolds admitting a semi-symmetric non-metric connection, arXiv:1801.03000v1 [math.DG] 9 Jan 2018.
  • [14] S. K. Chaubey and R. H. Ojha, On a semi-symmetric non-metric connection, Filomat 26 (2) (2012), 269-275.
  • [15] A. Taleshian and A. A. Hosseinzadeh, Some curvature properties of Kenmotsu manifolds, Proc. of the Nat. Academy of Sci. 85 (2015), 407-413.
  • [16] A. Basari and C. Murathan, On generalized f􀀀recurrent Kenmotsu manifolds, Fen Derg. 3 (1) (2008), 91-97.
  • [17] H. Ozturk, N. Aktan and C. Murathan, On a􀀀Kenmotsu manifolds satisfying certain conditions, Applied sciences 12 (2010), 115-126.
  • [18] K. Yano, Concircular geometry I, Concircular transformation, Proc. Imp. Acad. Tokyo 16 (1940), 195-200.
  • [19] K. Yano, Concircular geometry I, Imp. Acad. Sci. of Japan 16 (1940), 195-200.
  • [20] A. Friedmann and J. A. Schouten, ¨U ber die geometrie der halbsymmetrischen ¨ ubertragung, Math. Zeitschr 21 (1924), 211-223.
  • [21] H. A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc. 34 (1932), 27-50.
  • [22] K. Yano, On semi-symmetric metric connection, Rev. Roumaine de Math. Pures et Appl. 15 (1970), 1579-1586.
  • [23] J. V. Narlikar, General relativity and gravitation, The Macmillan co. of India, 1978.
  • [24] H. Stephani, General relativity-An introduction to the theory of gravitational field, Cambridge Univ. Press, Cambridge, 1982.
  • [25] D. E. Blair, Contact manifolds in Riemannian Geometry, Lecture Notes in Mathematics, 509, Springer-Verlag, Berlin, 1976.
  • [26] M. Kon, Invariant submanifolds in Sasakian manifolds, Math. Ann. 219 (1976), 277-290.
  • [27] S. K. Chaubey and A. Kumar, Semi-symmetric metric T-connection in an almost contact metric manifold, International Mathematical Forum 5 (23) (2010), 1121-1129.
  • [28] A. Sharfuddin and S. I. Husain, Semi-symmetric metric connections in almost contact manifolds, Tensor N. S. 30 (1976), 133-139.
  • [29] T. Imai, Notes on semi-symmetric metric connections, Tensor N. S. 24 (1972), 293-296.
  • [30] R. S. Mishra and S. N. Pandey, Semi-symmetric metric connections in an almost contact manifold, Indian J. Pure Appl. Math. 9 (6) (1978), 570-580.
  • [31] A. Berman, Concircular curvature tensor of a semi-symmetric metric connection in a Kenmotsu manifold, Thai J. of Mathematics 13 (1) (2015), 245-257.
  • [32] Sunil Yadav and D. L. Suthar, On three-dimensional quasi-Sasakian manifolds admitting semi-symmetric metric connection, international Journal of Physical Sciences 8 (17) (2013), 754-758.
  • [33] P. Alegre, D. E. Blair and A. Carriazo, Generalized Sasakian Space forms, Israel J. of Math. 141 (2004), 157-183.
  • [34] U. K. Kim, Conformally flat generalized Sasakian-space forms and locally symmetric generalized Sasakian-space forms, Note Mat. 26 (2006), 55–67.
  • [35] T. Takahashi, Sasakian f􀀀symmetric spaces, Tohoku Math. J. 29 (1977), 91-113

Study of Kenmotsu manifolds with semi-symmetric metric connection

Year 2018, , 89 - 97, 26.06.2018
https://doi.org/10.32323/ujma.427238

Abstract

The present paper deals with the study of Kenmotsu manifolds equipped with a semi-symmetric metric connection. The properties of $\eta-$parallel Ricci tensor, globally symmetric and $\phi-$symmetric Kenmotsu manifolds with the semi-symmetric metric connection are evaluated. In the end, we construct an example of a $3-$dimensional Kenmotsu manifold admitting semi-symmetric metric connection and verify our some results.

References

  • [1] Robert Osserman, Curvature in the Eighties, The American mathematical monthly 97 (8), (1990), 731-756.
  • [2] ´E . Cartan, Surune classe remarquable d’espaces de Riemannian, Bull. Soc. Math. France 54 (1926), 214- 264.
  • [3] ´E . Cartan, Le cons sur la g ´eeom´ etrie des espaces de Riemann, 2nd ed., Paris, 1946.
  • [4] B. O’ Neill, Semi-Riemannian geometry with applications to the relativity, Academic Press, New York- London, 1983.
  • [5] M. M. Boothby and R. C. Wong, On contact manifolds, Anna. Math. 68 (1958), 421-450.
  • [6] S. Sasaki and Y. Hatakeyama, On differentiable manifolds with certain structures which are closely related to almost contact structure, Tohoku Math. J. 13 (1961), 281-294.
  • [7] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24 (1972), 93-103.
  • [8] S. K. Chaubey and A. A. Shaikh, On 3-dimensional Lorentzian concircular structure manifolds, Commun. Korean Math. Soc., 33 (2018) https://doi.org/10.4134/CKMS.c180044.
  • [9] S. K. Chaubey and R. H. Ojha, On the m-projective curvature tensor of a Kenmotsu manifold, Differential Geometry - Dynamical Systems 12 (2010), 52-60.
  • [10] S. K. Chaubey, S. Prakash and R. Nivas, Some properties of m􀀀projective curvature tensor in Kenmotsu manifolds, Bulletin of Math Analysis and Applications 4 (2012), 48-56.
  • [11] S. K. Chaubey and C. S. Prasad, On generalized f􀀀recurrent Kenmotsu manifolds, TWMS J. App. Eng. Math. 5 (1) (2015), 1-9.
  • [12] S. K. Yadav, S. K. Chaubey and D. L. Suthar, Certain results on almost Kenmotsu (k;m;n)􀀀spaces, Konuralp Journal of Mathematics 6 (1) (2018) 128-133.
  • [13] S. K. Chaubey, A. C. Pandey, N. V. C. Shukla, Some properties of Kenmotsu manifolds admitting a semi-symmetric non-metric connection, arXiv:1801.03000v1 [math.DG] 9 Jan 2018.
  • [14] S. K. Chaubey and R. H. Ojha, On a semi-symmetric non-metric connection, Filomat 26 (2) (2012), 269-275.
  • [15] A. Taleshian and A. A. Hosseinzadeh, Some curvature properties of Kenmotsu manifolds, Proc. of the Nat. Academy of Sci. 85 (2015), 407-413.
  • [16] A. Basari and C. Murathan, On generalized f􀀀recurrent Kenmotsu manifolds, Fen Derg. 3 (1) (2008), 91-97.
  • [17] H. Ozturk, N. Aktan and C. Murathan, On a􀀀Kenmotsu manifolds satisfying certain conditions, Applied sciences 12 (2010), 115-126.
  • [18] K. Yano, Concircular geometry I, Concircular transformation, Proc. Imp. Acad. Tokyo 16 (1940), 195-200.
  • [19] K. Yano, Concircular geometry I, Imp. Acad. Sci. of Japan 16 (1940), 195-200.
  • [20] A. Friedmann and J. A. Schouten, ¨U ber die geometrie der halbsymmetrischen ¨ ubertragung, Math. Zeitschr 21 (1924), 211-223.
  • [21] H. A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc. 34 (1932), 27-50.
  • [22] K. Yano, On semi-symmetric metric connection, Rev. Roumaine de Math. Pures et Appl. 15 (1970), 1579-1586.
  • [23] J. V. Narlikar, General relativity and gravitation, The Macmillan co. of India, 1978.
  • [24] H. Stephani, General relativity-An introduction to the theory of gravitational field, Cambridge Univ. Press, Cambridge, 1982.
  • [25] D. E. Blair, Contact manifolds in Riemannian Geometry, Lecture Notes in Mathematics, 509, Springer-Verlag, Berlin, 1976.
  • [26] M. Kon, Invariant submanifolds in Sasakian manifolds, Math. Ann. 219 (1976), 277-290.
  • [27] S. K. Chaubey and A. Kumar, Semi-symmetric metric T-connection in an almost contact metric manifold, International Mathematical Forum 5 (23) (2010), 1121-1129.
  • [28] A. Sharfuddin and S. I. Husain, Semi-symmetric metric connections in almost contact manifolds, Tensor N. S. 30 (1976), 133-139.
  • [29] T. Imai, Notes on semi-symmetric metric connections, Tensor N. S. 24 (1972), 293-296.
  • [30] R. S. Mishra and S. N. Pandey, Semi-symmetric metric connections in an almost contact manifold, Indian J. Pure Appl. Math. 9 (6) (1978), 570-580.
  • [31] A. Berman, Concircular curvature tensor of a semi-symmetric metric connection in a Kenmotsu manifold, Thai J. of Mathematics 13 (1) (2015), 245-257.
  • [32] Sunil Yadav and D. L. Suthar, On three-dimensional quasi-Sasakian manifolds admitting semi-symmetric metric connection, international Journal of Physical Sciences 8 (17) (2013), 754-758.
  • [33] P. Alegre, D. E. Blair and A. Carriazo, Generalized Sasakian Space forms, Israel J. of Math. 141 (2004), 157-183.
  • [34] U. K. Kim, Conformally flat generalized Sasakian-space forms and locally symmetric generalized Sasakian-space forms, Note Mat. 26 (2006), 55–67.
  • [35] T. Takahashi, Sasakian f􀀀symmetric spaces, Tohoku Math. J. 29 (1977), 91-113
There are 35 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Sudhakar Chaubey

Sunil Kr Yadav

Publication Date June 26, 2018
Submission Date May 25, 2018
Acceptance Date June 20, 2018
Published in Issue Year 2018

Cite

APA Chaubey, S., & Yadav, S. K. (2018). Study of Kenmotsu manifolds with semi-symmetric metric connection. Universal Journal of Mathematics and Applications, 1(2), 89-97. https://doi.org/10.32323/ujma.427238
AMA Chaubey S, Yadav SK. Study of Kenmotsu manifolds with semi-symmetric metric connection. Univ. J. Math. Appl. June 2018;1(2):89-97. doi:10.32323/ujma.427238
Chicago Chaubey, Sudhakar, and Sunil Kr Yadav. “Study of Kenmotsu Manifolds With Semi-Symmetric Metric Connection”. Universal Journal of Mathematics and Applications 1, no. 2 (June 2018): 89-97. https://doi.org/10.32323/ujma.427238.
EndNote Chaubey S, Yadav SK (June 1, 2018) Study of Kenmotsu manifolds with semi-symmetric metric connection. Universal Journal of Mathematics and Applications 1 2 89–97.
IEEE S. Chaubey and S. K. Yadav, “Study of Kenmotsu manifolds with semi-symmetric metric connection”, Univ. J. Math. Appl., vol. 1, no. 2, pp. 89–97, 2018, doi: 10.32323/ujma.427238.
ISNAD Chaubey, Sudhakar - Yadav, Sunil Kr. “Study of Kenmotsu Manifolds With Semi-Symmetric Metric Connection”. Universal Journal of Mathematics and Applications 1/2 (June 2018), 89-97. https://doi.org/10.32323/ujma.427238.
JAMA Chaubey S, Yadav SK. Study of Kenmotsu manifolds with semi-symmetric metric connection. Univ. J. Math. Appl. 2018;1:89–97.
MLA Chaubey, Sudhakar and Sunil Kr Yadav. “Study of Kenmotsu Manifolds With Semi-Symmetric Metric Connection”. Universal Journal of Mathematics and Applications, vol. 1, no. 2, 2018, pp. 89-97, doi:10.32323/ujma.427238.
Vancouver Chaubey S, Yadav SK. Study of Kenmotsu manifolds with semi-symmetric metric connection. Univ. J. Math. Appl. 2018;1(2):89-97.

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