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arXiv · 1808.05317

Sphere theorems and eigenvalue pinching without positive Ricci curvature assumption

Masayuki Aino
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Abstract

Considering the almost rigidity of the Obata theorem, we generalize Petersen and Aubry's sphere theorem about eigenvalue pinching without assuming the positivity of Ricci curvature, only assuming $Ric\geq-Kg$ and $diam\leq D$ for some positive constants $K>0$ and $D>0$.

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Masayuki Aino. 2018-08-16. Sphere theorems and eigenvalue pinching without positive Ricci curvature assumption. https://doi.org/10.1007/s00526-019-1588-y

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