Abstract
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
.
Funder
Japan Society for the Promotion of Science
Publisher
Springer Science and Business Media LLC
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