On a Riemannian invariant of Chen type

Teodor Oprea

On a Riemannian invariant of Chen type

Differential Geometry 2007-05-23 v1 Optimization and Control

Authors: Teodor Oprea

Abstract

In [6] we proved Chen's inequality regarded as a problem of constrained maximum. In this paper we introduce a Riemannian invariant obtained from Chen's invariant, replacing the sectional curvature by the Ricci curvature of k-order. This invariant can be estimated, in the case of submanifolds M in space forms $\widetilde{M}(c)$ , varying with c and the mean curvature of M in $\widetilde{M}(c)$ . A improuvement of this inequality in the Lagrangian case is obtained.

Keywords

riemannian invariant chen invariant ricci curvature submanifold space form mean curvature lagrangian

Cite

@article{arxiv.math/0605321,
  title  = {On a Riemannian invariant of Chen type},
  author = {Teodor Oprea},
  journal= {arXiv preprint arXiv:math/0605321},
  year   = {2007}
}

Comments

The paper is submitted to Rocky Mountain Journal of Mathematics

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