On Yau rigidity theorem for minimal submanifolds in spheres

In this paper, we investigate the well-known Yau rigidity theorem for minimal submanifolds in spheres. Using the parameter method of Yau and the DDVV inequality verified by Lu and Ge-Tang, we prove that if M is an n-dimensional oriented compact minimal submanifold in the unit sphere S n+p , and if Here sgn() is the standard sign function. We also extend the rigidity theorem above to the case where M is a compact submanifold with parallel mean curvature in a space form.