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TRANS-SASAKIAN MANIFOLDS SATISFYING CERTAIN CONDITIONS

Year 2019, Volume: 9 Issue: 2, 305 - 314, 01.06.2019

Abstract

The objective of the present paper is to study the properties of special weakly Ricci symmetric and generalized Ricci recurrent trans Sasakian manifolds.

References

  • [1] Blair, D. E., (1976), Contact manifolds in Riemannian Geometry, Lecture Notes in Mathematics, Vol. 509, Springer-Verlag, Berlin.
  • [2] Patterson, E. M., (1952), Some theorems on Ricci-recurrent spaces, J. London Math. Soc., 27, 287-295.
  • [3] Sitaramayya, M., (1973), Curvature tensors in K¨ahler manifolds, Trans. Amer. Math. Soc., 183, 341- 353.
  • [4] Janssens, D. and Vanhacke, L., (1981), Almost contact structures and curvature tensors, Kodai Math. J., 4, 1-27.
  • [5] Dragomir, S. and Ornea, L., (1998), Locally conformal K¨ahler geometry, Progress in Mathematics, 155, Birkhauser Boston, Inc., Boston, MA.
  • [6] Chen, B. Y. and Yano, K., (1972), Hypersurfaces of conformally flat spaces, Tensor N. S., 26, 318-322.
  • [7] Ojha, R. H., (1975), A note on the M-projective curvature tensor, Indian J. Pure Applied Math., 8, No. (1-2), 1531-1534.
  • [8] Ojha, R. H., (1973), On Sasakian manifold, Kyungpook Math. J., 13, 211-215.
  • [9] Pokhariyal, G. P. and Mishra, R. S., (1971), Curvature tensor and their relativistic significance II, Yokohama Mathematical Journal, 19, 97-103.
  • [10] Chaubey, S. K. and Ojha, R. H., (2010), On the m-projective curvature tensor of a Kenmotsu manifold, Differential Geometry-Dynamical Systems, 12, 52-60.
  • [11] Chaubey, S. K., (2011), Some properties of LP-Sasakian manifolds equipped with m−projective curvature tensor, Bull. of Math. Anal. and Appl., 3 (4), 50-58.
  • [12] Chaubey, S. K., Prakash, S. and Nivas, R., (2012), Some properties of m−projective curvature tensor in Kenmotsu manifolds, Bull. of Math. Anal. and Appl., Volume 4 (3), 48-56.
  • [13] Chaubey, S. K., (2012), On weakly m−projectively symmetric manifolds, Novi Sad J. Math., Vol. 42, No. 1, 67-79.
  • [14] Blair, D. E. and Oubina, J. A., 1990), Conformal and related changes of metric on the product of almost contact contact metric manifolds, Publications Matemaliques, 34, 199-207.
  • [15] Tanno, S., (1971), Curvature tensors and non-existence of Killing vectors, Tensor, N. S., 22, 387-394.
  • [16] Tanno, S., (1969), The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J., 21, 21-38.
  • [17] Gray, A. and Hervella, L. M. , (1980), The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl., 123 (4) (1980), 35-58.
  • [18] Kenmotsu, K., (1972), A class of almost contact Riemannian manifolds, Tohoku Math. J., 24, 93-103.
  • [19] Oubina, J. A., (1985), New classes of contact metric structures, Publ. Math. Debrecen, 32 (3-4), 187-193.
  • [20] China, D. and Gonzales, C., (1987), Curvature relations in trans-Sasakian manifolds, Proceedings of the XIIth Poruguese-Spanish Conference of Mathematics, Vol. II (Potuguese) (Braga, 1987), 564-571, Univ. Minho, Braga.
  • [21] De, U. C. and Sarkar, A., (2008), On three dimensional trans-Sasakian manifolds, Extracta Math., 23 (3), 265-277.
  • [22] Marrero, J. C., (1992), The local structure of trans-Sasakian manifolds, Ann. Mat. Pure Appl., 162 (4), 77-86.
  • [23] De, U. C. and Tripathi, M. M. , (2003), Ricci tensor in 3−dimensional trans-Sasakian manifolds, Kyungpook Math. J., 43, 1-9.
  • [24] Bagewadi, C. S. and Venkatesha, (2007), Some curvature tensors on trans-Sasakian manifolds, Turk. J. Math., 30, 1-11.
  • [25] Bagewadi, C. S. and Kumar, Girish , (2004), Note on trans-Sasakian manifolds, Tensor N. S., 65 (1), 80-88.
  • [26] Kim, J. S., Prasad, R. and Tripathi, M. M., (2002), On generalized Ricci-recurrent trans Sasakian manifolds, J. Korean Math. Soc., 39 (6), 953-961.
  • [27] De, U. C., Guha, N. and Kamilya, D., (1995), On generalized Ricci-recurrent manifolds, Tensor N. S., 56, 312-317.
  • [28] De, U. C. and Mallick, S., (2012), Space times admitting m−projective curvature tensor, Bulg. J. Phys., 39, 331-338.
  • [29] Taleshian, A. and Asghari, N., (2012), On the m−projective tensor of P-Sasakian manifolds, J. of Phy. Sci., 16, 107-116.
  • [30] Singh, H. and Khan, Q., (2001), On special weakly symmetric Riemannian manifolds, Publ. Math. Debrecen, 58 (3), 523-536.
  • [31] Khan, Q., (2004), On conharmonically and special weakly Ricci symmetric Sasakian manifolds, Novi Sad J. Math., 34 (1), 71-77.
  • [32] Deszcz, R.,Verstraelen L. and Yaprak, S., (1994), Warped products realizing a certain condition of pseudo-symmetric type imposed on the curvature tensor, Chin. J. Math., 22 (2), 139-157.
  • [33] Vranceanu, Gh., (1968), Lecons des Geometric Differential, 4, Ed. de I’Academie, Bucharest.
  • [34] Mocanu, A. L., (1987), Les varietes a courbure quasi-constant de type Vranceanu, Lucr. Conf. Nat. de Geom. Si Top, Tirgoviste.
  • [35] Chaubey, S. K. and Prasad, C. S., (2015), On Generalized φ−Recurrent Kenmotsu Manifolds, TWMS J. App. Eng. Math. 5 (1), 1-9.
  • [36] Chaubey, S. K., (2017), Existence of N(k)−quasi Einstein manifolds, Facta Universitatis (NIS), Se. Math. Inform, (Accepted).
  • [37] Prakash, A., (2010), m−projectively recurrent LP-Sasakian manifolds, Indian Journal of Mathematics, 52 (1), 47-56.
  • [39] Singh, A., Kumar, R., Prakash, A. and Khare, S. (2015), On a Pseudo projective φ−recurrent Sasakian manifolds, Journal of Mathematics and Computer Science, 14(4), 309-314.
  • [40] Narain, D., Prakash, A. and Prasad, B. (2009), A pseudo projective curvature tensor on a Lorentzian para-Sasakian manifolds, Analele Stiintifice Ale Universitatii Al.I.Cuza Din Iasi (S.N.) Mathematica, Tomul LV fase.2, 275-284.
Year 2019, Volume: 9 Issue: 2, 305 - 314, 01.06.2019

Abstract

References

  • [1] Blair, D. E., (1976), Contact manifolds in Riemannian Geometry, Lecture Notes in Mathematics, Vol. 509, Springer-Verlag, Berlin.
  • [2] Patterson, E. M., (1952), Some theorems on Ricci-recurrent spaces, J. London Math. Soc., 27, 287-295.
  • [3] Sitaramayya, M., (1973), Curvature tensors in K¨ahler manifolds, Trans. Amer. Math. Soc., 183, 341- 353.
  • [4] Janssens, D. and Vanhacke, L., (1981), Almost contact structures and curvature tensors, Kodai Math. J., 4, 1-27.
  • [5] Dragomir, S. and Ornea, L., (1998), Locally conformal K¨ahler geometry, Progress in Mathematics, 155, Birkhauser Boston, Inc., Boston, MA.
  • [6] Chen, B. Y. and Yano, K., (1972), Hypersurfaces of conformally flat spaces, Tensor N. S., 26, 318-322.
  • [7] Ojha, R. H., (1975), A note on the M-projective curvature tensor, Indian J. Pure Applied Math., 8, No. (1-2), 1531-1534.
  • [8] Ojha, R. H., (1973), On Sasakian manifold, Kyungpook Math. J., 13, 211-215.
  • [9] Pokhariyal, G. P. and Mishra, R. S., (1971), Curvature tensor and their relativistic significance II, Yokohama Mathematical Journal, 19, 97-103.
  • [10] Chaubey, S. K. and Ojha, R. H., (2010), On the m-projective curvature tensor of a Kenmotsu manifold, Differential Geometry-Dynamical Systems, 12, 52-60.
  • [11] Chaubey, S. K., (2011), Some properties of LP-Sasakian manifolds equipped with m−projective curvature tensor, Bull. of Math. Anal. and Appl., 3 (4), 50-58.
  • [12] Chaubey, S. K., Prakash, S. and Nivas, R., (2012), Some properties of m−projective curvature tensor in Kenmotsu manifolds, Bull. of Math. Anal. and Appl., Volume 4 (3), 48-56.
  • [13] Chaubey, S. K., (2012), On weakly m−projectively symmetric manifolds, Novi Sad J. Math., Vol. 42, No. 1, 67-79.
  • [14] Blair, D. E. and Oubina, J. A., 1990), Conformal and related changes of metric on the product of almost contact contact metric manifolds, Publications Matemaliques, 34, 199-207.
  • [15] Tanno, S., (1971), Curvature tensors and non-existence of Killing vectors, Tensor, N. S., 22, 387-394.
  • [16] Tanno, S., (1969), The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J., 21, 21-38.
  • [17] Gray, A. and Hervella, L. M. , (1980), The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl., 123 (4) (1980), 35-58.
  • [18] Kenmotsu, K., (1972), A class of almost contact Riemannian manifolds, Tohoku Math. J., 24, 93-103.
  • [19] Oubina, J. A., (1985), New classes of contact metric structures, Publ. Math. Debrecen, 32 (3-4), 187-193.
  • [20] China, D. and Gonzales, C., (1987), Curvature relations in trans-Sasakian manifolds, Proceedings of the XIIth Poruguese-Spanish Conference of Mathematics, Vol. II (Potuguese) (Braga, 1987), 564-571, Univ. Minho, Braga.
  • [21] De, U. C. and Sarkar, A., (2008), On three dimensional trans-Sasakian manifolds, Extracta Math., 23 (3), 265-277.
  • [22] Marrero, J. C., (1992), The local structure of trans-Sasakian manifolds, Ann. Mat. Pure Appl., 162 (4), 77-86.
  • [23] De, U. C. and Tripathi, M. M. , (2003), Ricci tensor in 3−dimensional trans-Sasakian manifolds, Kyungpook Math. J., 43, 1-9.
  • [24] Bagewadi, C. S. and Venkatesha, (2007), Some curvature tensors on trans-Sasakian manifolds, Turk. J. Math., 30, 1-11.
  • [25] Bagewadi, C. S. and Kumar, Girish , (2004), Note on trans-Sasakian manifolds, Tensor N. S., 65 (1), 80-88.
  • [26] Kim, J. S., Prasad, R. and Tripathi, M. M., (2002), On generalized Ricci-recurrent trans Sasakian manifolds, J. Korean Math. Soc., 39 (6), 953-961.
  • [27] De, U. C., Guha, N. and Kamilya, D., (1995), On generalized Ricci-recurrent manifolds, Tensor N. S., 56, 312-317.
  • [28] De, U. C. and Mallick, S., (2012), Space times admitting m−projective curvature tensor, Bulg. J. Phys., 39, 331-338.
  • [29] Taleshian, A. and Asghari, N., (2012), On the m−projective tensor of P-Sasakian manifolds, J. of Phy. Sci., 16, 107-116.
  • [30] Singh, H. and Khan, Q., (2001), On special weakly symmetric Riemannian manifolds, Publ. Math. Debrecen, 58 (3), 523-536.
  • [31] Khan, Q., (2004), On conharmonically and special weakly Ricci symmetric Sasakian manifolds, Novi Sad J. Math., 34 (1), 71-77.
  • [32] Deszcz, R.,Verstraelen L. and Yaprak, S., (1994), Warped products realizing a certain condition of pseudo-symmetric type imposed on the curvature tensor, Chin. J. Math., 22 (2), 139-157.
  • [33] Vranceanu, Gh., (1968), Lecons des Geometric Differential, 4, Ed. de I’Academie, Bucharest.
  • [34] Mocanu, A. L., (1987), Les varietes a courbure quasi-constant de type Vranceanu, Lucr. Conf. Nat. de Geom. Si Top, Tirgoviste.
  • [35] Chaubey, S. K. and Prasad, C. S., (2015), On Generalized φ−Recurrent Kenmotsu Manifolds, TWMS J. App. Eng. Math. 5 (1), 1-9.
  • [36] Chaubey, S. K., (2017), Existence of N(k)−quasi Einstein manifolds, Facta Universitatis (NIS), Se. Math. Inform, (Accepted).
  • [37] Prakash, A., (2010), m−projectively recurrent LP-Sasakian manifolds, Indian Journal of Mathematics, 52 (1), 47-56.
  • [39] Singh, A., Kumar, R., Prakash, A. and Khare, S. (2015), On a Pseudo projective φ−recurrent Sasakian manifolds, Journal of Mathematics and Computer Science, 14(4), 309-314.
  • [40] Narain, D., Prakash, A. and Prasad, B. (2009), A pseudo projective curvature tensor on a Lorentzian para-Sasakian manifolds, Analele Stiintifice Ale Universitatii Al.I.Cuza Din Iasi (S.N.) Mathematica, Tomul LV fase.2, 275-284.
There are 39 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

S. K. Chaubey This is me

Publication Date June 1, 2019
Published in Issue Year 2019 Volume: 9 Issue: 2

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