The nullity of a compact minimal hypersurface in a compact symmetric space of rank one (Q1772574)

The principal results of the paper are the following: Theorem. Let \(M\) be a compact minimal hypersurface in the Cayley projective plane. Then its nullity satisfies \text{null}\((M)\) \(\geqslant 16\). When the nullity of \(M\) is equal to \(16\), then \(M\) must be a minimal geodesic hypersphere. Theorem. Let \(X\) be a compact symmetric space of rank one and \(M\) a compact minimal hypersurface 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 \(X.\)