The nullity of a compact minimal hypersurface in a compact symmetric space of rank one

Abstract

We determine a compact minimal hypersuface with the least nullity in the Cayley projective plane. Combining this with the preceding results, we conclude the following: Let X be a compact symmetric space of rank one and M a compact minimal hypersuface in X. Then the nullity of M is bounded from below by the dimension of X. When the nullity of M is equal to the dimension of X, M must be a minimal geodesic hypersphere in X. Conversely,the nullity of a minimal geodesic hypersphere in X is equal to the dimension of X.