Spherical CR-manifolds of dimension 3 |
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Authors: | Elisha Falbel Nikolay Gusevskii |
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Affiliation: | (1) Instituto de Matemática e Estatística, Universidade de São Paulo, CP 20570, 01317-970 Sao Paulo, Brasil;(2) Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, 22460-320 Rio de Janeiro, Brasil |
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Abstract: | A sphericalCR-structure on a smooth (2n–1)-manifoldM is a maximal collection of distinguished charts modeled on the boundary H n of the complex hyperbolic space, where coordinate changes are restrictions of transformations from PU(n, 1). There exists a development map , where is the universal covering ofM, which is a local diffeomorphism. We study properties of the development maps and holonomy groups of sphericalCR-structures on compact 3-dimensional manifolds. We also give constructions of fundamental domains for some discrete subgroups of PU(2, 1). |
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