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Vol. 50 No. 2 (2024)
Serdica Mathematical Journal

Surveys

A survey on pluriclosed and CYT metrics

https://doi.org/10.55630/serdica.2024.50.103-124

Published 13-08-2024

  • Anna Fino
    • ,
  • Gueo Grantcharov

Anna Fino
Università degli studi di Torino and Florida International University

Gueo Grantcharov
Florida International University

Abstract

A Hermitian metric on a complex manifold is called pluriclosed if the torsion of the associated Bismut connection is closed, and it is said to be CYT if the Bismut Ricci form vanishes. In this paper, we survey recent results on pluriclosed and CYT metrics and review some constructions of compact non-Kähler manifolds.

2020 Mathematics Subject Classification:

53C55, 53C05, 22E25, 53C30, 53C44

Keywords

Bismut connection, Hermitian metric, pluriclosed metric, CYT metric

Full text

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