Lichnerowicz-Obata Estimate, Almost Parallel p-form and Almost Product Manifolds
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AbstractWe 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 ($$2\le p \le n/2$$ 2 ≤ p ≤ n / 2 ) in $$L^2$$ L 2 -sense, and give a Gromov-Hausdorff approximation to a product $$S^{n-p}\times X$$ S n - p × X under some pinching conditions when $$2\le p<n/2$$ 2 ≤ p < n / 2 .
2007 ◽
Vol 57
(2)
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pp. 467-472
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1985 ◽
Vol 100
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pp. 11-48
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2011 ◽
Vol 29
(3)
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pp. 374-387
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