Remarks on an inequality involving the normal scalar curvature

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 ${\mathbb{C}}^n$.

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

References in corpus (1)

• On the DDVV Conjecture and the Comass in Calibrated Geometry (I)

Cited by in corpus (5)

• Natural Intrinsic Geometrical Symmetries
• $\delta$-Invariants, Inequalities of Submanifolds and Their Applications
• DDVV-type inequality for skew-symmetric matrices and Simons-type inequality for Riemannian submersions
• On some conjectures by Lu and Wenzel
• On the DDVV Conjecture and the Comass in Calibrated Geometry (I)