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

Masayuki Aino

Published 2019-04-13Version 1

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 ($2\leq p \leq n/2$) in $L^2$-sense, and give a pinching result about the almost equality case when $2\leq p<n/2$.