Maximal Complexifications of Certain Riemannian Homogeneous Manifolds
نویسندگان
چکیده
Let M = G/K be a Riemannian homogeneous manifold with dimCG C = dimRG , where G C denotes the universal complexification of G. Under certain extensibility assumptions on the geodesic flow of M , we give a characterization of the maximal domain of definition in TM for the adapted complex structure and show that it is unique. For instance, this can be done for 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 definitions for the adapted complex structure which are neither holomorphically separable, nor holomorphically convex.
منابع مشابه
Maximal Complexifications of Certain Homogeneous Riemannian Manifolds
Let M = G/K be a homogeneous Riemannian manifold with dimCGC = dimRG, where GC denotes the universal complexification of G. Under certain extensibility assumptions on the geodesic flow of M , we give a characterization of the maximal domain of definition in TM for the adapted complex structure and show that it is unique. For instance, this can be done for generalized Heisenberg groups and natur...
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