T^2-invariant Einstein metrics on closed 4-manifolds

Kyle Broder; Ramiro A. Lafuente

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arXiv · 2610.18219

T^2-invariant Einstein metrics on closed 4-manifolds

Kyle Broder·Ramiro A. Lafuente

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Abstract

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.

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BibTeX RIS

Kyle Broder, Ramiro A. Lafuente. 2026-10-13. T^2-invariant Einstein metrics on closed 4-manifolds. https://arxiv.org/abs/2610.18219

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