Mathematical Research Letters

Volume 29 (2022)

Number 5

Deformation of Hermitian metrics

Pages: 1485 – 1497



Man-Chun Lee (Department of Mathematics, Chinese University of Hong Kong)

Ka-Fai Li (Morningside Center of Mathematics, Academy of Mathematics and Systems Science, C.A.S., Beijing, China)


In this work, we study the deformation of Hermitian metrics and the respective Chern curvature tensors. By adapting the conformal perturbation method of Aubin and Ehrlich to Hermitian setting, we prove that Hermitian metrics with quasi-positive (resp. quasi-negative) second Chern–Ricci curvature is conformal to a Hermitian metric with positive (resp. negative) second Chern–Ricci curvature.

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Received 4 July 2020

Accepted 30 September 2020

Published 21 April 2023