TY  - Type of reference 
TI  - First Chen Inequality for General Warped Product Submanifolds of a Riemannian Space Form and Applications 
AU  - Abdulqader MUSTAFA 
AU  - Cenap OZEL 
AU  - Alexander PIGAZZINI 
AU  - Ramandeep KAUR 
AU  - Gauree SHANKER 
AB  - 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. 
DO  - 10.21494/ISTE.OP.2023.0979 
JF  - Advances in Pure and Applied Mathematics 
KW  - Mean curvature vector,  δ-invariant,  scalar curvature,  warped products,  minimal submanifolds,  Riemannian space forms, Mean curvature vector,  δ-invariant,  scalar curvature,  warped products,  minimal submanifolds,  Riemannian space forms,  
L1  - http://openscience.fr/IMG/pdf/iste_apam23v14n3_2.pdf 
LA  - en 
PB  - ISTE OpenScience 
DA  - 2023/06/15 
SN  - 1869-6090 
TT  - Première inégalité de Chen pour des produits tordus de sous-variétés d’un espace forme riemannien et applications 
UR  - http://openscience.fr/First-Chen-Inequality-for-General-Warped-Product-Submanifolds-of-a-Riemannian 
IS  - Issue 3 (June 2023) 
VL  - 14 
ER  -