The first part of this book provides a self-contained and accessible introduction to the subject
in the general setting of pseudo-Riemannian manifolds and their non-degenerate …

The famous Nash embedding theorem was aimed for in the hope that if Riemannian
manifolds could be regarded as Riemannian submanifolds, this would then yield the …

Abstract Recently, B.-Y. Chen studied warped products which are CR-submanifolds in
Kaehler manifolds and established general sharp inequalities for CR-warped products in …

On Chen invariants and inequalities in quaternionic geometry | Journal of Inequalities and
Applications Skip to main content SpringerLink Account Menu Find a journal Publish with us …

The main purpose of this paper is to explain the two strings of new type of Riemannian
curvature invariants and the sharp inequalities, involving these invariants and the squared …

Abstract Recently, B.-Y. Chen studied warped products which are CR-submanifolds in
Kaehler manifolds and established general sharp inequalities for CR-warped products in …

Recently, Chen established a sharp relationship between the Ricci curvature and the
squared mean curvature for a submanifold in a Riemannian space form with arbitrary …

Chen (1999) established a sharp relationship between the Ricci curvature and the squared
mean curvature for a submanifold in a Riemanian space form with arbitrary codimension …

One of the most fundamental problems in submanifold theory is to establish simple
relationships between intrinsic and extrinsic invariants of the submanifolds (cf.[6]). A general …

Roughly speaking, an ideal immersion of a Riemannian manifold into a space form is an
isometric immersion which produces the least possible amount of tension from the ambient …