Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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A. Mustafa - C. Ozel - A. Pigazzini - R. Kaur - G. Shanker

First Chen Inequality for General Warped Product Submanifolds of a Riemannian Space Form and Applications

created by pigazzini on 15 Apr 2022
modified on 23 Sep 2023


Published Paper

Inserted: 15 apr 2022
Last Updated: 23 sep 2023

Journal: Adv. Pure Appl. Math.
Volume: 14
Number: 3
Pages: 22-40
Year: 2023


In this paper, the first Chen inequality is proved for general warped product submanifolds in Riemannian space forms, this inequality involves intrinsic invariants (δ-invariant and sectional curvature) controlled by an extrinsic one (the mean curvature vector), which provides an answer for Problem 1. As a geometric application, this inequality is applied to derive a necessary condition for the immersed submanifold to be minimal in Riemannian space forms, which presents a partial answer for the well-known problem proposed by S.S. Chern, Problem 2. For further research directions, we address a couple of open problems; namely Problem 3 and Problem 4.

Keywords: δ-invariant; warped product; minimal submanifolds; Riemannian space forms

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