Deformation of Hermitian metrics
arXiv:2006.15526
Abstract
In this work, we study the deformation of Hermitian metrics with Chern connection. 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 can be deformed to one with positive (resp. negative) curvature.
arXiv comment10 pages; references added
References in corpus (10)
- On the evolution of a Hermitian metric by its Chern-Ricci form
- Negative Holomorphic curvature and positive canonical bundle
- An extension of a theorem of Wu-Yau
- RC-positive metrics on rationally connected manifolds
- A parabolic flow of balanced metrics
- On the image of MRC fibrations of projective manifolds with semi-positive holomorphic sectional curvature
- RC-positivity and the generalized energy density I: Rigidity
- Comparison and vanishing theorems for Kähler manifolds
- On morphisms of compact Kähler manifolds with semi-positive holomorphic sectional curvature
- Compact Kähler manifolds with quasi-positive second Chern-Ricci curvature