On Einstein, Hermitian 4-Manifolds
Differential Geometry
2010-10-04 v1
Abstract
Let (M,h) be a compact 4-dimensional Einstein manifold, and suppose that h is Hermitian with respect to some complex structure J on M. Then either (M,J,h) is Kaehler-Einstein, or else, up to rescaling and isometry, it is one of the following two exceptions: the Page metric on CP2 # (-CP2), or the Einstein metric on CP2 # 2 (-CP2) constructed in Chen-LeBrun-Weber.
Cite
@article{arxiv.1010.0238,
title = {On Einstein, Hermitian 4-Manifolds},
author = {Claude LeBrun},
journal= {arXiv preprint arXiv:1010.0238},
year = {2010}
}
Comments
33 pages, 3 figures