Abstract
In this paper we give a survey of main results concerning Chen inequalities for submanifolds in quaternionic space forms and propose some open problems in the field for further research. AMS Subject Classification:53C15, 53C25, 53C40.
Highlights
The theory of Chen invariants, initiated by Prof
In [ ], the present author obtained the generalization of the first Chen inequality to the case of slant submanifolds in quaternionic space forms as follows
In [ ], Chen extended the notion of Ricci curvature to k-Ricci curvature for a Riemannian manifold and established a sharp relationship between k-Ricci curvatures and the shape operator and a sharp relationship between k-Ricci curvatures and the squared mean curvature for an n-dimensional Riemannian submanifold in a real space form M with constant sectional curvature c
Summary
The theory of Chen invariants, initiated by Prof. B.-Y. In [ ], the present author obtained the generalization of the first Chen inequality to the case of slant submanifolds in quaternionic space forms as follows.
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