Remarks on an inequality involving the normal scalar curvature

Details Remarks on an inequality involving the normal scalar curvature Remarks on an inequality involving the normal scalar curvature

2006-10-24

arxiv.org/abs/math/0610721v2

Mathematics

Differential Geometry

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

Scientific paper

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 $\mathbb C^n$.

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