WARPED PRODUCT OF RIEMANNIAN MANIFOLDS

Document Type : Original Article

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Abstract

ABSTRACT:
The sectional curvature of the Riemannian warped product mani-fold is derived in terms of the original ones. The secand fundemental form and totally geodesic submanifolds in warped product manifolds are introduced. We study the important example RXfR (warped plane) as an application. The Livi-civita connection on RXfR is derived. Morever, we discuss its godesics and Gauss curvarture with specific  forms of f (x). The concepts of coloring and folding by curvature are introduced on the warped plane. Illustrating figures are given.

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