Abstract
Warped products are the most natural and fruitful generalization of Riemannian products. Such products play very important roles in differential geometry and in general relativity. After Bishop and O’Neill’s 1969 article, there have been many works done on warped products from intrinsic point of view during the last fifty years. In contrast, the study of warped products from extrinsic point of view was initiated around the beginning of this century by the first author in a series of his articles. In particular, he established an optimal inequality for an isometric immersion of a warped product N1×fN2 into any Riemannian manifold Rm(c) of constant sectional curvature c which involves the Laplacian of the warping function f and the squared mean curvature H2. Since then, the study of warped product submanifolds became an active research subject, and many papers have been published by various geometers. The purpose of this article is to provide a comprehensive survey on the study of warped product submanifolds which are closely related with this inequality, done during the last two decades.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference138 articles.
1. Manifolds of negative curvature
2. Differential Geometry of Warped Product Manifolds and Submanifolds;Chen,2017
3. Semi-Riemannian Geometry with Applications to Relativity;O’Neill,1983
4. Geometry of warped product submanifolds: A survey;Chen;J. Adv. Math. Stud.,2013
5. The Imbedding Problem for Riemannian Manifolds
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