Parallel vector fields on the noninvariant hypersurface of a Sasakian manifold

2012/10/11 by S. K. Srivastava, Srivastava, Sachin Kumar, Alok Kumar Srivastava +3
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1210.3128

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 M with (ϕ, g, u, v, λ)- 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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