@ARTICLE{10.21494/ISTE.OP.2023.0979, 

TITLE={First Chen Inequality for General Warped Product Submanifolds of a Riemannian Space Form and Applications}, 
  
AUTHOR={Abdulqader MUSTAFA, Cenap OZEL, Alexander PIGAZZINI, Ramandeep KAUR, Gauree SHANKER, }, 
	
JOURNAL={Advances in Pure and Applied Mathematics}, 
	
VOLUME={14}, 

NUMBER={Issue 3 (June 2023)}, 
	
YEAR={2023}, 

URL={http://openscience.fr/First-Chen-Inequality-for-General-Warped-Product-Submanifolds-of-a-Riemannian}, 
	
DOI={10.21494/ISTE.OP.2023.0979}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={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.}}