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

Auteurs : Abdulqader MUSTAFA, Cenap OZEL, Alexander PIGAZZINI, Ramandeep KAUR, Gauree SHANKER,  

Revue : Advances in Pure and Applied Mathematics 

Numéro : Issue 3 (June 2023) 

Volume : 14 

Date : 2023/06/15 

DOI : 10.21494/ISTE.OP.2023.0979 

ISSN : 1869-6090 

Résumé : 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 Chen’s Problem 1 relating to establish simple relationships between the main extrinsic invariants and the main intrinsic invariants of a submanifold. 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. 

Éditeur : ISTE OpenScience