Complex nilmanifolds and K\"ahler-like connections
Differential Geometry
2022-07-18 v1
Abstract
In this note, we analyze the question of when will a complex nilmanifold have K\"ahler-like Strominger (also known as Bismut), Chern, or Riemannian connection, in the sense that the curvature of the connection obeys all the symmetries of that of a K\"ahler metric. We give a classification in the first two cases and a partial description in the third case. It would be interesting to understand these questions for all Lie-Hermitian manifolds, namely, Lie groups equipped with a left invariant complex structure and a compatible left invariant metric.
Cite
@article{arxiv.1904.09707,
title = {Complex nilmanifolds and K\"ahler-like connections},
author = {Quanting Zhao and Fangyang Zheng},
journal= {arXiv preprint arXiv:1904.09707},
year = {2022}
}