Transversal hypersurfaces of (LCS)n-manifolds
Main Article Content
Abstract
The object of the present paper is to study some properties oftransversal hypersurfaces of (LCS)n-manifolds. Further, we investigate some characterizations on geodesic hypersurfaces of (LCS)n-manifolds. We also prove that if M is a transversal hypersurface of an (LCS)n-manifold with a parallel vector eld V and an (1; 1) tensor eld f with zero eigen value, then M is totally geodesic.
Article Details
How to Cite
Ahmad, M., & Shaikh, A.
(2018).
Transversal hypersurfaces of (LCS)n-manifolds.
Acta Mathematica Universitatis Comenianae, 87(1), 107-116.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/609/581
Issue
Section
Articles
References
1: Ahmad, M., Jun, J. B. and Haseeb, A., Hypersurfaces of an almost r-paracontact Riemannian manifolds endowed with a quarter symmetric metric connection, Bull. Korean Math. Soc. 46 (3) (2009), 477-487.
2: Ahmad, M., Ozgur, C., Hypersurfaces of an almost r-paracontact Riemannian manifolds endowed with a semi-symmetric non-metric connection, Result Math. 55 (2009), 1-10.
3: Ahmad, M., Ozgur, C., Haseeb, A., Hypersurfaces of an almost r-paracontact Riemannian manifolds endowed with a quarter symmetric non-metric connection, Kyungpook Math. J. 49 (2009), 533-543.
4: Atceken, M., On geometry of submanifolds of of (LCS)n manifolds, Int. J. Math. Math. Sci. 2012. doi:10.1155/2012/304647.
5: Blair, D.E. and Ludden, G.D., Hypersurfaces in almost contact manifold, Tohoku Math. J. 22(1969), 3554-362.
6: Blair, D.E., Ludden, G.D. and Yano, K., Induced structures on submanifolds, Kodai Math. Sem. Rep. 22(1970),188-198.
7: Eum, S.S., On complex hypersurfaces in normal almost contact spaces, Tensor 19(1968), 45-50.
8: Goldberg, S. I. and Yano, K., Non-invariant hypersurfaces of almost contact manifolds, J. Math. Soc. Japan, 22(1970), 25-35.
9: Motsumoto, K.: On Lorentzian paracontact manifolds. Bull. of Yamagata Univ. Nat. Sci. 12 (2), (1989), 151-156.
10: Narain, D. and Yadav, S., On weak concircular symmetries of (LCS)2n+1-manifolds, Glob. J. Sci. Front. Res. 12 (2012), 85-94.
11: Okumura, M., Certain hypersurfaces of an odd-dimensional sphere, Tohoku Math. J. 19(1967), 381-395.
12: Prasad, R., On transversal hypersurfaces with (f; g; u; v; \lambda)-structure manifolds, Bull. Cal. Math. Soc. 99 (4) (2007), 375-384.
13: Prasad, R. and Tripathi, M.M., Transversal hypersurfaces of Kenmotsu manifolds, Indian J. Pure. Appl. Math. 34 (3) (2003), 443-452.
14: Prasad, R. and Yadav, S.P., Transversal hypersurfaces with (f; g; u; v; \lambda)-structure of a nearly trans-Sasakian manifold, Advances in Pure. Appl. Math. 7 (2) (2016), 115-121.
15: Prakasha, D.G., On Ricci \eta-recurrent (LCS)n-manifolds, Acta Univ. Apulensis, 24 (2010), 109-118.
16: Shaikh, A.A., On Lorentzian almost paracontact manifolds with a structure of concircular type, Kyungpook Math. J. 43 (2) (2003, 305-314.
17: Shaikh, A.A. and Ahmad, H., Some transformations on (LCS)n-manifolds, Tsukuba J. Math. 38 (2014), 1-24.
18: Shaikh, A.A. and Baishya, K. K., On concircular structure spacetimes II, American J. Appl. Sci. 12 (2) (2006), 1790-1794.
19: Shaikh, A.A., Basu, T. and Eyasmin, S., On locally \phi-symmetric (LCS)_n-manifolds, Int. J. Pure Appl. Math. 41 (8) (2007), 1161-1170.
20: Shaikh, A.A. and Binh, T.Q., On weakly symmetric (LCS)n-manifolds, J. Adv. Math. Studies 2 (2009), 75-90.
21: Shaikh, A.A. and Hui, S.K., On generalized \phi-recurrent (LCS)n-manifolds, Proceedings of the AIP conferences, 1309 (2010), 419-429.
22: Sreenivasa, G.T., Ventessa, Bhagewadi, C.S., Some results on (LCS)2n+1-manifolds, Bull. Math. Ann. Appl. 1 (3) (2009), 64-70.
23: Tashiro, Y., On contact structure of hypersurfaces in complex manifolds, I Tohoku Math. J. 15 (1963), 62-78.
24: Yadav, S.K. and Dwivedi, P.K., Suther, D., On (LCS)2n+1-manifolds satisfying conditions on the concircular curvature tensor, Thai. J. Math. 9 (3) (2011), 597-603.
25: Yamaguchi, S., On hypersurfaces in Sasakian manifold, Kodai Math. Sem. Rep. 21(1969), 64-72.
26: Yano, K. and Ki., U-Hang, On quasi-normal (f; g; u; v; \lambda)-structures, Kodai Math. Sem. Rep. 24(1972), 121-130.
27: Yano, K., Eum, S.E. and Ki,U-Hang., On transversal hypersurfaces of an almost contact manifold, Kodai Math. Sem. Rep. 24(1972), 459-470.
28: Yano, K. and Okumura, M., Invariant hypersurfaces of manifold with (f; g; u; v; \lambda)-structures, Kodai Math. Sem. Rep. 23(1971), 290-304.
29: Yano, K. and Okumura, M., On (f; g; u; v; )-structures, Kodai Math. Sem. Rep. 22 (1970), 401-423.
30: Yano, K. and Okumura, M., Invariant submanifolds with (f; g; u; v; \lambda)-structures, Kodai Math. Sem. Rep. 24(1972), 75-90.
2: Ahmad, M., Ozgur, C., Hypersurfaces of an almost r-paracontact Riemannian manifolds endowed with a semi-symmetric non-metric connection, Result Math. 55 (2009), 1-10.
3: Ahmad, M., Ozgur, C., Haseeb, A., Hypersurfaces of an almost r-paracontact Riemannian manifolds endowed with a quarter symmetric non-metric connection, Kyungpook Math. J. 49 (2009), 533-543.
4: Atceken, M., On geometry of submanifolds of of (LCS)n manifolds, Int. J. Math. Math. Sci. 2012. doi:10.1155/2012/304647.
5: Blair, D.E. and Ludden, G.D., Hypersurfaces in almost contact manifold, Tohoku Math. J. 22(1969), 3554-362.
6: Blair, D.E., Ludden, G.D. and Yano, K., Induced structures on submanifolds, Kodai Math. Sem. Rep. 22(1970),188-198.
7: Eum, S.S., On complex hypersurfaces in normal almost contact spaces, Tensor 19(1968), 45-50.
8: Goldberg, S. I. and Yano, K., Non-invariant hypersurfaces of almost contact manifolds, J. Math. Soc. Japan, 22(1970), 25-35.
9: Motsumoto, K.: On Lorentzian paracontact manifolds. Bull. of Yamagata Univ. Nat. Sci. 12 (2), (1989), 151-156.
10: Narain, D. and Yadav, S., On weak concircular symmetries of (LCS)2n+1-manifolds, Glob. J. Sci. Front. Res. 12 (2012), 85-94.
11: Okumura, M., Certain hypersurfaces of an odd-dimensional sphere, Tohoku Math. J. 19(1967), 381-395.
12: Prasad, R., On transversal hypersurfaces with (f; g; u; v; \lambda)-structure manifolds, Bull. Cal. Math. Soc. 99 (4) (2007), 375-384.
13: Prasad, R. and Tripathi, M.M., Transversal hypersurfaces of Kenmotsu manifolds, Indian J. Pure. Appl. Math. 34 (3) (2003), 443-452.
14: Prasad, R. and Yadav, S.P., Transversal hypersurfaces with (f; g; u; v; \lambda)-structure of a nearly trans-Sasakian manifold, Advances in Pure. Appl. Math. 7 (2) (2016), 115-121.
15: Prakasha, D.G., On Ricci \eta-recurrent (LCS)n-manifolds, Acta Univ. Apulensis, 24 (2010), 109-118.
16: Shaikh, A.A., On Lorentzian almost paracontact manifolds with a structure of concircular type, Kyungpook Math. J. 43 (2) (2003, 305-314.
17: Shaikh, A.A. and Ahmad, H., Some transformations on (LCS)n-manifolds, Tsukuba J. Math. 38 (2014), 1-24.
18: Shaikh, A.A. and Baishya, K. K., On concircular structure spacetimes II, American J. Appl. Sci. 12 (2) (2006), 1790-1794.
19: Shaikh, A.A., Basu, T. and Eyasmin, S., On locally \phi-symmetric (LCS)_n-manifolds, Int. J. Pure Appl. Math. 41 (8) (2007), 1161-1170.
20: Shaikh, A.A. and Binh, T.Q., On weakly symmetric (LCS)n-manifolds, J. Adv. Math. Studies 2 (2009), 75-90.
21: Shaikh, A.A. and Hui, S.K., On generalized \phi-recurrent (LCS)n-manifolds, Proceedings of the AIP conferences, 1309 (2010), 419-429.
22: Sreenivasa, G.T., Ventessa, Bhagewadi, C.S., Some results on (LCS)2n+1-manifolds, Bull. Math. Ann. Appl. 1 (3) (2009), 64-70.
23: Tashiro, Y., On contact structure of hypersurfaces in complex manifolds, I Tohoku Math. J. 15 (1963), 62-78.
24: Yadav, S.K. and Dwivedi, P.K., Suther, D., On (LCS)2n+1-manifolds satisfying conditions on the concircular curvature tensor, Thai. J. Math. 9 (3) (2011), 597-603.
25: Yamaguchi, S., On hypersurfaces in Sasakian manifold, Kodai Math. Sem. Rep. 21(1969), 64-72.
26: Yano, K. and Ki., U-Hang, On quasi-normal (f; g; u; v; \lambda)-structures, Kodai Math. Sem. Rep. 24(1972), 121-130.
27: Yano, K., Eum, S.E. and Ki,U-Hang., On transversal hypersurfaces of an almost contact manifold, Kodai Math. Sem. Rep. 24(1972), 459-470.
28: Yano, K. and Okumura, M., Invariant hypersurfaces of manifold with (f; g; u; v; \lambda)-structures, Kodai Math. Sem. Rep. 23(1971), 290-304.
29: Yano, K. and Okumura, M., On (f; g; u; v; )-structures, Kodai Math. Sem. Rep. 22 (1970), 401-423.
30: Yano, K. and Okumura, M., Invariant submanifolds with (f; g; u; v; \lambda)-structures, Kodai Math. Sem. Rep. 24(1972), 75-90.