On the evolution of a Hermitian metric by its Chern-Ricci form

Details On the evolution of a Hermitian metric by its Chern-Ricci form On the evolution of a Hermitian metric by its Chern-Ricci form

2011-12-31

arxiv.org/abs/1201.0312v2

Mathematics

Differential Geometry

37 pages, v2 minor changes in wording

Scientific paper

We consider the evolution of a Hermitian metric on a compact complex manifold by its Chern-Ricci form. This is an evolution equation first studied by M. Gill, and coincides with the Kahler-Ricci flow if the initial metric is Kahler. We find the maximal existence time for the flow in terms of the initial data. We investigate the behavior of the flow on complex surfaces when the initial metric is Gauduchon, on complex manifolds with negative first Chern class, and on some Hopf manifolds. Finally, we discuss a new estimate for the complex Monge-Ampere equation on Hermitian manifolds.

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