Complex nilmanifolds and Kahler-like connections

[摘要] In this note, we analyze the question of when will a complex nilmanifold have Kahler-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 Kahler metric. We give a classification in the second case and a partial description in the first and 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. (C) 2019 Elsevier B.V. All rights reserved.

[发布日期] 2019-12-01

[关键词] Kahler-like;Strominger connection;Chern connection;Riemannian connection;Pluriclosed metric;Nilmanifold