Abstract

Abstract:

In this paper we study a particular version of the {\it Hermitian curvature flow} (HCF) over a compact complex Hermitian manifold $(M,g,J)$. We prove that if the initial metric has Griffiths positive (non-negative) Chern curvature $\Omega$, then this property is preserved along the flow. On a manifold with Griffiths non-negative Chern curvature the HCF has nice regularization properties, in particular, for any $t>0$ the zero set of $\Omega(\xi,\bar\xi,\eta,\bar\eta)$ becomes invariant under certain {\it torsion-twisted} parallel transport.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1751-1775
Launched on MUSE
2019-11-02
Open Access
No
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