On the curvature of minimal submanifolds in a sphere

Abstract

S. T. Yau proved in Amer. J. Math.97 (1975), p. 95, Theorem 15 that if the sectional curvature of an n-dimensional compact minimal submanifold in the (n + p)-dimensional unit sphere is everywhere greater than (p - 1)/(2 p - 1), then this minimal submanifold is totally geodesic. In this note we improve this bound for the case p ≥ 2 to (3 p - 2)/(6 p). © 1995 Kluwer Academic Publishers.