A proof of the DDVV conjecture and its equality case (Q953125)

The authors give a proof of the so called DDVV conjecture (i.e., the conjecture of \textit{P. J. De Smet, F. Dillen, L. Verstraelen} and \textit{L. Vrancken} [Arch. Math., Brno 35, No.~2, 115--128 (1999; Zbl 1054.53075)]) involving the scalar curvature, the normal scalar curvature and the mean curvature on a submanifold of a real space form. The problem of the equality case is also solved.