Submanifolds of Riemannian Product Manifolds

Authors: MEHMET ATÇEKEN

Abstract: In this paper, we study the geometry of the semi-invariant submanifolds of a Riemannian product manifold. Fundamental properties of these type submanifolds such as the integrability of the distributions D, D^{\bot} and mixed-geodesic property are studied. Finally, necessary and sufficient conditions are given on a semi-invariant submanifold of Riemannian product manifold to be D-geodesic and D^{\bot}-geodesic.

Keywords: Riemannian Product Manifold, Real Space Form, Locally Riemannian Product and Curvature-Invariant Submanifold

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