PreprintCC BY 4.0arXiv
T^2-invariant Einstein metrics on closed 4-manifolds
Abstract
We construct T2-invariant Einstein metrics with positive Ricci curvature on #_m(S^2 x S^2) for every integer m>1. These provide infinite family of Einstein metrics on closed $4$-manifolds with λ>0, which are in addition not Hermitian. We further establish the uniqueness of the T2-invariant Einstein metrics on S4, CP^2, S^2 x S^2, and CP^2#\bar{CP}^2.
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BibTeX
@misc{broder2026t2invariant,
title = {{T^2-invariant Einstein metrics on closed 4-manifolds}},
author = {Kyle Broder and Ramiro A. Lafuente},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18219},
eprint = {2610.18219},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18219},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - T^2-invariant Einstein metrics on closed 4-manifolds
AU - Kyle Broder
AU - Ramiro A. Lafuente
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18219
UR - https://arxiv.org/abs/2610.18219
AB - We construct T^2-invariant Einstein metrics with positive Ricci curvature on #_m(S^2 x S^2) for every integer m>1. These provide infinite family of Einstein metrics on closed $4$-manifolds with λ>0, which are in addition not Hermitian. We further establish the uniqueness of the T^2-invariant Einstein metrics on S^4, CP^2, S^2 x S^2, and CP^2#\bar{CP}^2.
ER -