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arXiv · 1904.09707

Complex nilmanifolds and Kähler-like connections

Quanting Zhao·Fangyang Zheng
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Abstract

In this note, we analyze the question of when will a complex nilmanifold have Kähler-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 Kähler 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.

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Quanting Zhao, Fangyang Zheng. 2019-04-22. Complex nilmanifolds and Kähler-like connections. https://arxiv.org/abs/1904.09707

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