English

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).

Keywords

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

R2 v1 2026-06-21T16:25:16.083Z