New inhomogeneous Bismut Hermitian-Einstein threefolds with large symmetry group
Abstract
We study compact non-Kähler Bismut Hermitian-Einstein threefolds whose connected full group of holomorphic isometries acts with cohomogeneity one. We prove that the Lie algebra of this group is isomorphic to ℝ3⊕su(2) or ℝ2⊕su(2), unless the Bismut connection is flat. We then focus on the first case, where we determine the possible singular isotropy algebras and reduce the Bismut Hermitian-Einstein condition to a system of ordinary differential equations. We obtain explicit solutions satisfying suitable smoothness conditions, that yield families of compact and complete non-compact non-Kähler Bismut Hermitian-Einstein threefolds with non-constant scalar curvature and non-zero Bismut curvature, including examples on S3× S3 and S3× S1×ℝ2, respectively. We also investigate the topology of the compact examples and determine the asymptotic scalar curvature of the non-compact ones. Moreover, we prove the existence of a smooth deformation of a Bismut-flat Samelson structure on S3× S3 through non-Kähler Bismut Hermitian-Einstein structures that are not Bismut-flat. The regularity of the constructed compact examples is also investigated.
Related
- A gluing construction of Z-extremal Kähler metrics and new examples of Bismut Hermitian-Einstein $3$-folds
- Curvature characterization of Hermitian manifolds with Bismut parallel torsion
- On Compact Hermitian Surfaces With Positive Strominger-Bismut Sectional Curvature
- Hermitian threefolds with constant holomorphic sectional curvature
- Compactification of parabolic Hermitian--Einstein moduli spaces on complex surfaces
BibTeX
@misc{podesta2026inhomogeneous,
title = {{New inhomogeneous Bismut Hermitian-Einstein threefolds with large symmetry group}},
author = {Fabio Podestà and Alberto Raffero},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37102},
eprint = {2610.37102},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37102},
}
RIS
TY - UNPB
TI - New inhomogeneous Bismut Hermitian-Einstein threefolds with large symmetry group
AU - Fabio Podestà
AU - Alberto Raffero
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37102
UR - https://arxiv.org/abs/2610.37102
AB - We study compact non-Kähler Bismut Hermitian-Einstein threefolds whose connected full group of holomorphic isometries acts with cohomogeneity one. We prove that the Lie algebra of this group is isomorphic to ℝ^3⊕su(2) or ℝ^2⊕su(2), unless the Bismut connection is flat. We then focus on the first case, where we determine the possible singular isotropy algebras and reduce the Bismut Hermitian-Einstein condition to a system of ordinary differential equations. We obtain explicit solutions satisfying suitable smoothness conditions, that yield families of compact and complete non-compact non-Kähler Bismut Hermitian-Einstein threefolds with non-constant scalar curvature and non-zero Bismut curvature, including examples on S^3× S^3 and S^3× S^1×ℝ^2, respectively. We also investigate the topology of the compact examples and determine the asymptotic scalar curvature of the non-compact ones. Moreover, we prove the existence of a smooth deformation of a Bismut-flat Samelson structure on S^3× S^3 through non-Kähler Bismut Hermitian-Einstein structures that are not Bismut-flat. The regularity of the constructed compact examples is also investigated.
ER -