Maximal Complexifications of Certain Riemannian Homogeneous Manifolds

Details Maximal Complexifications of Certain Riemannian Homogeneous Manifolds Maximal Complexifications of Certain Riemannian Homogeneous Manifolds

2002-06-07

arxiv.org/abs/math/0206071v1

Mathematics

Complex Variables

18 pages, LaTeX-file

Scientific paper

A characterization of maximal domains of existence of adapted complex structures for Riemannian homogeneous manifolds under certain extensibility assumptions on their geodesic flow is given. This is applied to generalized Heisenberg groups and naturally reductive Riemannian homogeneous spaces. As an application it is shown that the case of generalized Heisenberg groups yields examples of maximal domains of definition for the adapted complex structure which are are neither holomorphically separable, nor holomorphically convex.

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