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

Masayuki Aino

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

Differential Geometry 2021-01-07 v5

Authors: Masayuki Aino

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 ( $2\leq p \leq n/2$ ) in $L^2$ -sense, and give an almost decomposition result of the manifold under some pinching conditions when $2\leq p<n/2$ .

Keywords

laplacian eigenvalues laplacian eigenfunctions

Cite

@article{arxiv.1904.06533,
  title  = {Lichnerowicz-Obata Estimate, Almost Parallel $p$-form and Almost Product Manifolds},
  author = {Masayuki Aino},
  journal= {arXiv preprint arXiv:1904.06533},
  year   = {2021}
}

Comments

66 pages v2:some error corrected, Appendix B added, v3:some error corrected, v4:some proofs simplified, v5: some error corrected, some descriptions simplified

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