On the fundamental group of steady gradient Ricci solitons with nonnegative sectional curvature

Yuxing Deng; Yuehan Hao

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arXiv · 2412.07452

On the fundamental group of steady gradient Ricci solitons with nonnegative sectional curvature

Yuxing Deng·Yuehan Hao

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Abstract

In this paper, we study the fundamental group of the complete steady gradient Ricci soliton with nonnegative sectional curvature. We prove that the fundamental group of such a Ricci soliton is either trivial or infinite. As a corollary, we show that an $n$-dimensional complete $\kappa$-noncollapsed steady gradient Ricci soliton with nonnegative sectional curvature must be diffeomorphic to $\mathbb{R}^n$.

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BibTeX RIS

Yuxing Deng, Yuehan Hao. 2024-12-10. On the fundamental group of steady gradient Ricci solitons with nonnegative sectional curvature. https://arxiv.org/abs/2412.07452

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