Vol. 237, No. 1, 2008
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A proof of the DDVV conjecture and its equality case

Ge Jianquan & Tang Zizhou

Vol. 237 (2008), No. 1, 87-95
Abstract

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. We also solve the problem of its equality case.
Keywords

normal scalar curvature, mean curvature, commutator

Mathematical Subject Classification

Primary: 53C42, 15A45
Authors
Ge Jianquan
Department of Mathematical Sciences
Tsinghua University
Beijing 100084
China
Tang Zizhou
School of Mathematical Sciences
Laboratory of Mathematics and Complex Systems
Beijing Normal University
Beijing 100875
China