English

On Bismut--Ambrose--Singer manifolds

Differential Geometry 2026-05-05 v1 Complex Variables

Abstract

We investigate Bismut--Ambrose--Singer (BAS) manifolds, namely Hermitian manifolds whose Bismut connection has parallel torsion and parallel curvature. We first establish a canonical reduction theorem for complete, simply-connected BAS manifolds. We then classify simply-connected BAS manifolds in the three fundamental homogeneous settings: the compact case, the non-compact semisimple case, and the nilpotent case. Building on this, we construct BAS manifolds in which these three geometries are combined, generalizing all previously known examples. Finally we classify complete, simply-connected, pluriclosed BAS manifolds.

Keywords

Cite

@article{arxiv.2605.02485,
  title  = {On Bismut--Ambrose--Singer manifolds},
  author = {Giuseppe Barbaro and Francesco Pediconi},
  journal= {arXiv preprint arXiv:2605.02485},
  year   = {2026}
}

Comments

25 pages. Comments are welcome

R2 v1 2026-07-01T12:48:22.744Z