NDLI: Geometric Inequalities for Warped Products in Riemannian Manifolds

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Geometric Inequalities for Warped Products in Riemannian Manifolds

Content Provider	MDPI
Author	Chen, Bang-Yen Blaga, Adara
Copyright Year	2021
Description	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 $N1\timesfN2$ 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.
Starting Page	923
e-ISSN	22277390
DOI	10.3390/math9090923
Journal	Mathematics
Issue Number	9
Volume Number	9
Language	English
Publisher	MDPI
Publisher Date	2021-04-21
Access Restriction	Open
Subject Keyword	Mathematics Mathematical Physics Warped Products Warped Product Immersion Inequality Space Forms Space of Quasi-constant Curvature Eigenfunction Laplacian
Content Type	Text
Resource Type	Article

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