Ricci tensor of slant submanifolds in a quaternion projective space (Q544912)

The authors prove the following: Suppose that \(M\) is an \(n\)-dimensional \(\theta\)-slant submanifold in a quaternion projective space \(\mathbb QP^m (4c)\), then, for each unit vector \(X\in T_p M,\) the Ricci tensor \(S(X)\) satisfies the inequality \[ S(X)\leq \tfrac{n^2}{4}\,H^2 +(n-1)c + 9c \cos ^2\theta. \] Equality holds identically for all unit tangent vectors at \(p\) if and only if \(p\) is a totally geodesic point or \(n=2\) and \(M\) is a totally umbilical point.