Abstract
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.
Citation
Fei Huang. Hongwei Xu. Entao Zhao. "Differentiable pinching theorems for submanifolds via Ricci flow." Tohoku Math. J. (2) 67 (4) 531 - 540, 2015. https://doi.org/10.2748/tmj/1450798071
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