  Inspired by the Lichnerowicz-Obata theorem for the first eigenvalue of the
Laplacian, we define a new family of invariants $\{\Omega_k(g)\}$ for closed
Riemannian manifolds. The value of $\Omega_k(g)$ delicately reflects the
spherical part of the manifold. Indeed, $\Omega_1(g)$ and $\Omega_2(g)$
characterize the standard sphere.
