Tohoku Mathematical Journal

Differentiable pinching theorems for submanifolds via Ricci flow

Fei Huang, Hongwei Xu, and Entao Zhao

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Two differentiable pinching theorems are verified via the Ricci flow and stable currents. We first prove a differentiable sphere theorem for positively pinched submanifolds in a space form. Moreover, we obtain a differentiable sphere theorem for submanifolds in the sphere $\mathbb{S}^{n+p}$ under extrinsic restriction.

Article information

Tohoku Math. J. (2), Volume 67, Number 4 (2015), 531-540.

First available in Project Euclid: 22 December 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 53C40: Global submanifolds [See also 53B25]

Submanifolds differentiable sphere theorem Ricci flow stable current curvature pinching


Xu, Hongwei; Huang, Fei; Zhao, Entao. Differentiable pinching theorems for submanifolds via Ricci flow. Tohoku Math. J. (2) 67 (2015), no. 4, 531--540. doi:10.2748/tmj/1450798071.

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