A proof of the DDVV conjecture and its equality case

Abstract

In this paper, we give a proof of the DDVV conjecture which is a pointwise inequality involving the scalar curvature, the normal scalar curvature and the mean curvature on a submanifold of a real space form. Furthermore we solved the problem of its equality case.

10 pages,submitted, a revised version with minor corrections to Cor1.2