# Lie-algebraic curvature conditions preserved by the Hermitian curvature flow

@article{Ustinovskiy2017LiealgebraicCC,
title={Lie-algebraic curvature conditions preserved by the Hermitian curvature flow},
author={Yury Ustinovskiy},
journal={Mathematische Annalen},
year={2017},
volume={379},
pages={1713-1745}
}
The purpose of this paper is to prove that the Hermitian Curvature Flow (HCF) on an Hermitian manifold ( M ,  g ,  J ) preserves many natural curvature positivity conditions. Following ideas of Wilking (J Reine Angew Math 679:223–247, 2013), for an $$\text {Ad}\,{GL(T^{1,0}M)}$$ Ad G L ( T 1 , 0 M ) -invariant subset $$S\subset \text {End}\,(T^{1,0}M)$$ S ⊂ End ( T 1 , 0 M ) and a nice function $$F:\text {End}\,(T^{1,0}M)\rightarrow {\mathbb {R}}$$ F : End ( T 1 , 0 M ) → R we construct a…
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