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- W2567414058 abstract "In this paper we consider a Riemannian manifold (M;g) with a Killing vector fleld » and study the question of obtaining conditions under which its compact hypersurfaces admit a Killing vector fleld. The presence of the Killing vector fleld » on M, naturally gives rise to two special vector flelds ;, a smooth function ‰ and a (1;1)-tensor fleld ˆ on a compact hypersurface M of M. We prove that if the scalar curvatures of M and M are equal, M has positive Ricci curvature and the smooth function ‰ is a constant then is a Killing vector fleld on the compact hypersurface M. Our other result states that if M is totally umbilical hypersurface such that the Rcci curvature of M in the direction of the unit normal vector fleld is a positive constant, then » is tangential to M and is therefore Killing vector fleld on M." @default.
- W2567414058 created "2017-01-06" @default.
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- W2567414058 date "2011-01-01" @default.
- W2567414058 modified "2023-09-23" @default.
- W2567414058 title "Hypersurfaces of a Riemannian manifold with Killing vector fleld" @default.
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