Pages: 395-403
Date of Publication: 02-Feb-2018
Semi Parallel and Weyl-Semi Parallel Hypersurface of Tachibana Manifold
Author: Prabhat Narayan Singh, S. K. Dubey
Category: Engineering, Science and Mathematics
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Abstract:
In this paper, we have studied semi parallel and Weyl semi parallel para-Sasakian hypersurface of a Tachibana manifold. We have prove that para-Sasakian hypersurface of a Tachibana manifold is semi-parallel if and only if it is totally umbilical with negative unit mean curvature. Further we have prove that such a hypersurface is Weyl-semi-parallel if and only if it is either __ampersandsigneta;?Einstein manifold or semi-parallel. Some more results has been studied in this paper.
References:
J. Deprez : Semi-parallel surfaces in Euclidean space, J. Geom., 25 (1985), 192-200.
[2] J. Deprez : Semi-parallel hypersurfaces, Rend. Sem. Mat. Univers Politech. Torino, 44 (1986), 303-316.
[3] Ü Lumiste : Semi-symmetric submanifolds as the second order envelope of symmetric submanifolds, Proc. Estonian Acad. Sci. Phy. Math., 39 (1990), 1-8.
[4] F. Dillen : Semi-parallel hypersurfaces of real space form, Israel J. Math., 75 (1991), 193-202.
[5] A. C. Asperti, G. A. Lobos and F. Mercuri : Pseudo-parallel immersion in space forms, Math. Contemp., 17 (1999), 59-70.
[6] C. Özgür : Submanifolds satisfying some curvature conditions imposed on the Weyl-tensor, Bull. Austral. Math. Soc., 67 (1) (2003), 95-101.
[7] R. S. Mishra : Structures on differentiable manifold and their applications, Chandrama Prakashan, Allahabad, 1984.
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