Rigidity of complex projective spaces in Ricci shrinkers

TL;DR

This paper proves a rigidity result for Ricci shrinkers, showing that those close to complex projective spaces in the Gromov-Hausdorff sense are actually isometric to them, highlighting their geometric uniqueness.

Contribution

The paper establishes a new rigidity theorem for Ricci shrinkers near complex projective spaces, demonstrating their geometric stability and uniqueness.

Findings

Ricci shrinkers close to $( ext{CP}^N, g_{FS})$ are isometric to it

Gromov-Hausdorff closeness implies isometry for these spaces

Highlights the rigidity of complex projective spaces in Ricci shrinkers

Abstract

In this paper, we prove that any Ricci shrinker that is sufficiently close to $(\mathbb C P^N,g_{FS})$ in the Gromov-Hausdorff sense must itself be isometric to $(\mathbb C P^N,g_{FS})$.