Remarks on an inequality involving the normal scalar curvature

Franki Dillen; Johan Fastenakels; Joeri Van der Veken

Remarks on an inequality involving the normal scalar curvature

Differential Geometry 2007-10-31 v2

Authors: Franki Dillen , Johan Fastenakels , Joeri Van der Veken

Abstract

We study a pointwise inequality for submanifolds in real space forms involving the scalar curvature, the normal scalar curvature and the mean curvature. We translate it into an algebraic problem, allowing us to prove a slightly weaker version of it. We also prove the conjecture for certain types of submanifolds of $\mathbb C^n$ .

Keywords

submanifolds real space forms scalar curvature normal scalar curvature mean curvature pointwise inequality

Cite

@article{arxiv.math/0610721,
  title  = {Remarks on an inequality involving the normal scalar curvature},
  author = {Franki Dillen and Johan Fastenakels and Joeri Van der Veken},
  journal= {arXiv preprint arXiv:math/0610721},
  year   = {2007}
}

Comments

to appear in the Proceedings of the International Congress on Pure and Applied Differential Geometry PADGE2007

Remarks on an inequality involving the normal scalar curvature

Abstract

Keywords

Cite

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