## Tohoku Mathematical Journal

### Differentiable pinching theorems for submanifolds via Ricci flow

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 22 December 2015

https://projecteuclid.org/euclid.tmj/1450798071

Digital Object Identifier
doi:10.2748/tmj/1450798071

Mathematical Reviews number (MathSciNet)
MR3436540

Zentralblatt MATH identifier
1334.53025

#### Citation

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. https://projecteuclid.org/euclid.tmj/1450798071

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