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We show a Lichnerowicz-Obata type estimate for the first eigenvalue of theLaplacian of $n$-dimensional closed Riemannian manifolds with an almostparallel $p$-form ($2\leq p \leq n/2$) in $L^2$-sense, and give an almostdecomposition result of the manifold under some pinching conditions when $2\leqp<n/2$.

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