On doubly warped product immersions

Abstract

In this paper we study fundamental geometric properties of doubly warped product immersion which is an extension of warped product immersion. Moreover, we study geometric inequality for doubly warped products isometrically immersed in arbitrary Riemannian manifolds.

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• Chen's inequality for C-totally real submanifolds in a generalized $(\kappa ,\mu )$-space form