PreprintCC BY 4.0arXiv
Einstein metrics with torus symmetry on S4 and ℝ4
Abstract
This note gives direct proofs that, under an effective isometric T2 action, Einstein metrics on smooth homotopy four-spheres are round and complete Ricci-flat metrics on smooth manifolds homeomorphic to ℝ4 are Euclidean or positive one-center Taub--NUT, up to isometry, scaling, and orientation reversal.
Related
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- Quantized Einstein Metrics on S7 with SU(3)-Symmetry
- Stability and instability of torus-symmetric Einstein spacetimes with square-integrable connection
- Torus and Positive Mass stability for metrics with Ricci curvature lower bound
- Instability of conformally Kähler, Einstein metrics
BibTeX
@misc{chen2026einstein,
title = {{Einstein metrics with torus symmetry on $S^4$ and $\mathbb R^4$}},
author = {Xiuxiong Chen and Conghan Dong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12210},
eprint = {2610.12210},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12210},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Einstein metrics with torus symmetry on S^4 and ℝ^4
AU - Xiuxiong Chen
AU - Conghan Dong
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.12210
UR - https://arxiv.org/abs/2610.12210
AB - 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 ℝ^4 are Euclidean or positive one-center Taub--NUT, up to isometry, scaling, and orientation reversal.
ER -