Complex Surfaces with Cat(0) Metrics |
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| Authors: | Dmitri Panov |
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| Institution: | (1) Faculty of Mathematics, University of Bucharest, 14 Academiei str., 70109 Bucharest, Romania;(2) Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, Bucharest, Romania;(3) Department of Mathematics, University of Glasgow, 15 University Gardens, Glasgow, Scotland;(4) Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya, 25, Moscow, 117259, Russia |
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| Abstract: | We study complex surfaces with locally CAT(0) polyhedral K?hler metrics and construct such metrics on
\mathbbCP2{\mathbb{C}P^{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 unit 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
\mathbbCP2{\mathbb{C}P^{2}} of sufficiently high degree their desingularizations are of type K(π, 1). |
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