Work

Einstein metrics with torus symmetry on $S^4$ and $\mathbb R^4$

Year: 2026

Type: preprint

Abstract: This note gives direct proofs that, under an effective isometric $T^2$ action, Einstein metrics on smooth homotopy four-spheres are round and complete Ricci-flat metrics on smooth manifolds homeomorphic to $\mathbb R^4$ are Euclidean or positive one-center Taub--NUT, up to isometry, scaling, and orientation reversal.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.12210

Authors: Chen, Xiuxiong, Dong, Conghan

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7221188954

Cites: 2

Cited by:

Related to: 10