Certain results of $(LCS)_{n}$-manifolds endowed with $E$-Bochner curvature tensor
DOI:
https://doi.org/10.5269/bspm.65813Resumen
In this paper, we study geometry of $(LCS)_{n}$-manifold focusing on some conditions of $E$-Bochner curvature tensor. First, we describe an $E$-Bochner pseudo-symmetric $(LCS)_{n}$-manifold is never reduces to $E$-Bochner semi-symmetric manifold under the condition ($(\alpha^{2}-\rho)\neq0$). Next, we characterize certain results of $(LCS)_{n}$-manifold satisfying $B^{e}(U,V)\xi=0$, $B^{e}(\xi,V)\cdot B^{e}=0$ and $B^{e}(\xi,V)\cdot S=0$.
Referencias
1. Blair, D. E., On the geometric meaning of the Bochner tensor, Geom. Dedicata, 4, 33-38, (1975).
2. Bochner, S., Curvature and Betti numbers, Ann. Math. (2), 50(1), 77-93, (1949).
3. Boothby, W. M. and Wang, H. C., On contact manifolds, Ann. Math. (2) 68(3), 721-734, (1958).
4. Endo, H., On K-contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor, Colloq. Math., 62(2), 293-297, (1991).
5. Hui, S. K., On -pseudo Symmetries of (LCS)n-Manifolds, Kyungpook Math. J., 53, 285-294, (2013).
6. Hui, S. K. and Atceken, M., Contact warped product semi-slant submanifolds of (LCS)n-manifolds, Acta Univ. Sapientiae, Math., 3(2), 212-224, (2011).
7. Matsumoto, K., On Lorentzian almost paracontact manifolds, Bull. Yamagata Univ. Nat. Sci., 12, 151-156, (1989).
8. Matsumoto, M., and Chuman, G., On the C-Bochner tensor, TRU Math., 5, 21-30, (1969).
9. Mihai, I. and Rosca, R., On Lorentzian para-Sasakian manifolds, Classical Analysis, World Scientific Publ., Singapore, 155-169, (1992).
10. Naveen Kumar, R. T., Siva Kota Reddy, P., Venkatesha and Sangeetha, M., Certain Results on (k, μ)-Contact Metric Manifold endowed with Concircular Curvature Tensor, Commun. Math. Appl., 14(1), to appear, (2023).
11. Phalaksha Murthy, B., Naveen Kumar, R. T., Siva Kota Reddy, P. and Venkatesha, Extended Pseudo Projective Curvature Tensor on (LCS)n-Manifold, Proceedings of the Jangjeon Math. Soc., 25(3), 347-354, (2022).
12. Prakasha, D. G., On Ricci -recurrent (LCS)n-manifolds, Acta Universitatis Apulensis, 24, 109-118, (2010).
13. Somashekhara, P., Naveen Kumar, R. T., Siva Kota Reddy, P., Venkatesha and Alloush, K. A. A., Pseudo Projective Curvature Tensor on Generalized Sasakian Space Forms, Proceedings of the Jangjeon Math. Soc., 26, to appear, (2023).
14. Shaikh, A. A., On Lorentzian almost paracontact manifolds with a structure of the concircular type, Kyungpook Math. J., 43, 305–314, (2003).
15. Shaikh, A. A., Some results on (LCS)n-manifolds, J. Korean Math. Soc., 46, 449-461, (2009).
16. Shaikh, A. A. and Ahmad, H., Some transformations on (LCS)n-manifold, Tsukuba J. Math., 38, 1-24, (2014).
17. Shaikh, A. A. and Baishya, K. K., On concircular structure spacetimes, J. Math. Stat., 1, 129–132, (2005).
18. Shaikh, A. A. and Baishya, K. K., On concircular structure spacetimes II, American J. Appl. Sci., 3, 1790-1794, (2006).
19. Shaikh, A. A., Matsuyama, Y. and Hui, S. K., On invariant submanifolds of (LCS)n-manifolds, J. Egypt. Math. Soc., 24(2), 263-269, (2016).
20. Shukla, S. S. and Shukla, M. K., Slant Submanifolds of (LCS)n-manifolds, Kyungpook Math. J., 54, 667-676, (2014).
21. Sreenivasa, G. T., Venkatesha and Bagewadi, C. S., Some results on (LCS)2n+1-manifolds, Bull. Math. Analysis and Appl., 1(3), 64-70, (2009).
22. Venkatesha and Naveen Kumar, R. T., Some symmetric properties on (LCS)n-manifolds, Kyungpook Math. J., 55, 149-156, (2015). 
2. Bochner, S., Curvature and Betti numbers, Ann. Math. (2), 50(1), 77-93, (1949).
3. Boothby, W. M. and Wang, H. C., On contact manifolds, Ann. Math. (2) 68(3), 721-734, (1958).
4. Endo, H., On K-contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor, Colloq. Math., 62(2), 293-297, (1991).
5. Hui, S. K., On -pseudo Symmetries of (LCS)n-Manifolds, Kyungpook Math. J., 53, 285-294, (2013).
6. Hui, S. K. and Atceken, M., Contact warped product semi-slant submanifolds of (LCS)n-manifolds, Acta Univ. Sapientiae, Math., 3(2), 212-224, (2011).
7. Matsumoto, K., On Lorentzian almost paracontact manifolds, Bull. Yamagata Univ. Nat. Sci., 12, 151-156, (1989).
8. Matsumoto, M., and Chuman, G., On the C-Bochner tensor, TRU Math., 5, 21-30, (1969).
9. Mihai, I. and Rosca, R., On Lorentzian para-Sasakian manifolds, Classical Analysis, World Scientific Publ., Singapore, 155-169, (1992).
10. Naveen Kumar, R. T., Siva Kota Reddy, P., Venkatesha and Sangeetha, M., Certain Results on (k, μ)-Contact Metric Manifold endowed with Concircular Curvature Tensor, Commun. Math. Appl., 14(1), to appear, (2023).
11. Phalaksha Murthy, B., Naveen Kumar, R. T., Siva Kota Reddy, P. and Venkatesha, Extended Pseudo Projective Curvature Tensor on (LCS)n-Manifold, Proceedings of the Jangjeon Math. Soc., 25(3), 347-354, (2022).
12. Prakasha, D. G., On Ricci -recurrent (LCS)n-manifolds, Acta Universitatis Apulensis, 24, 109-118, (2010).
13. Somashekhara, P., Naveen Kumar, R. T., Siva Kota Reddy, P., Venkatesha and Alloush, K. A. A., Pseudo Projective Curvature Tensor on Generalized Sasakian Space Forms, Proceedings of the Jangjeon Math. Soc., 26, to appear, (2023).
14. Shaikh, A. A., On Lorentzian almost paracontact manifolds with a structure of the concircular type, Kyungpook Math. J., 43, 305–314, (2003).
15. Shaikh, A. A., Some results on (LCS)n-manifolds, J. Korean Math. Soc., 46, 449-461, (2009).
16. Shaikh, A. A. and Ahmad, H., Some transformations on (LCS)n-manifold, Tsukuba J. Math., 38, 1-24, (2014).
17. Shaikh, A. A. and Baishya, K. K., On concircular structure spacetimes, J. Math. Stat., 1, 129–132, (2005).
18. Shaikh, A. A. and Baishya, K. K., On concircular structure spacetimes II, American J. Appl. Sci., 3, 1790-1794, (2006).
19. Shaikh, A. A., Matsuyama, Y. and Hui, S. K., On invariant submanifolds of (LCS)n-manifolds, J. Egypt. Math. Soc., 24(2), 263-269, (2016).
20. Shukla, S. S. and Shukla, M. K., Slant Submanifolds of (LCS)n-manifolds, Kyungpook Math. J., 54, 667-676, (2014).
21. Sreenivasa, G. T., Venkatesha and Bagewadi, C. S., Some results on (LCS)2n+1-manifolds, Bull. Math. Analysis and Appl., 1(3), 64-70, (2009).
22. Venkatesha and Naveen Kumar, R. T., Some symmetric properties on (LCS)n-manifolds, Kyungpook Math. J., 55, 149-156, (2015). 
Descargas
Publicado
2024-05-08
Número
Sección
Research Articles
Licencia
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
