WARPED PRODUCT OF RIEMANNIAN MANIFOLDS | ||||
| The International Conference on Mathematics and Engineering Physics | ||||
| Article 11, Volume 3, International Conference on Engineering Mathematics and Physics (ICMEP-3), May 2006, Page 1-13 PDF (2.92 MB) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/icmep.2006.29914 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
| M. BELTAGY; S. SHENAWY | ||||
| 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. | ||||
| Keywords | ||||
| warped product; Curvature; Riemannian metric; Riemannian connection; geodesics | ||||
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