Compact Gauduchon-Flat Hermitian manifolds

Abstract: On a non-Kähler Hermitian manifold, the complex structure is not parallel with respect to the Levi-Civita connection. Instead, it is natural to consider non-symmetric connections compatible with both metric and complex structures. In the 90's, Gauduchon identified a canonical one-parameter family of such Hermitian connections which includes the Chern and Bismut connections. In this talk we will discuss some recent progress in understanding the geometry of these so-called Gauduchon connections, detailing a proof of a conjecture of Yang and Zheng. Namely that other than the Chern or Bismut cases, compact Hermitian manifolds with flat Gauduchon connections are Kähler.

differential geometry

Audience: researchers in the topic

Differential Geometry Seminar Torino

Series comments: This is a hybrid seminar organized by the Differential Geometry groups of Università and Politecnico di Torino.

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