Complex surfaces with CAT(0) metrics
Differential Geometry
2011-07-12 v2 Algebraic Geometry
Geometric Topology
Abstract
We study complex surfaces with locally CAT(0) polyhedral Kahler metrics and construct such metrics on CP^2 with various orbifold structures. In particular, in relation to questions of Gromov and Davis-Moussong we construct such metrics on a compact quotient of the two-dimensional unite complex ball. In the course of the proof of these results we give criteria for Sasakian 3-manifolds to be globally CAT(1). We show further that for certain Kummer coverings of CP^2 of sufficiently high degree their desingularizations are of type K(pi,1).
Cite
@article{arxiv.1010.1448,
title = {Complex surfaces with CAT(0) metrics},
author = {Dmitri Panov},
journal= {arXiv preprint arXiv:1010.1448},
year = {2011}
}
Comments
Revised version accepted in GAFA