Tohoku Mathematical Journal
2015

December
SECOND SERIES VOL. 67, NO. 4

Tohoku Math. J.
67 (2015), 531-540

Title DIFFERENTIABLE PINCHING THEOREMS FOR SUBMANIFOLDS VIA RICCI FLOW

Author Hongwei Xu, Fei Huang and Entao Zhao

(Received May 1, 2014, revised June 18, 2014)
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.

Mathematics Subject Classification. Primary 53C20; Secondary 53C40.

Key words and phrases. Submanifolds, differentiable sphere theorem, Ricci flow, stable current, curvature pinching.

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