Parallel vector fields on the noninvariant hypersurface of a Sasakian manifold

Sachin Kumar Srivastava; Alok Kumar Srivastava; Dhruwa Narain

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arXiv · 1210.3128

Parallel vector fields on the noninvariant hypersurface of a Sasakian manifold

Sachin Kumar Srivastava·Alok Kumar Srivastava·Dhruwa Narain

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Abstract

In 1970, Samuel I. Goldberg and Kentaro Yano defined the notion of noninvariant hypersurface of a Sasakian manifold [1]. In this paper we have studied the properties of parallel vector fields with respect to induced connection on the noninvariant hypersurface $M$ of a Sasakian manifold $\tilde M$ with $(\phi, g, u, v, \lambda)-$ structure and proved that if the vector field $V$ is parallel with respect to induced connection on $M$ then $M$ is totally geodesic.

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BibTeX RIS

Sachin Kumar Srivastava, Alok Kumar Srivastava, Dhruwa Narain. 2012-10-11. Parallel vector fields on the noninvariant hypersurface of a Sasakian manifold. https://arxiv.org/abs/1210.3128

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