Lichnerowicz-Obata Estimate, Almost Parallel $p$-form and Almost Product Manifolds

Abstract

We show a Lichnerowicz-Obata type estimate for the first eigenvalue of the Laplacian of n-dimensional closed Riemannian manifolds with an almost parallel p-form (2 ≤ p ≤ n/2) in L 2 -sense, and give an almost decomposition result of the manifold under some pinching conditions when 2 ≤ p < n/2.