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Maximal Complexifications of Certain Homogeneous Riemannian Manifolds

S. Halverscheid and A. Iannuzzi
Transactions of the American Mathematical Society
Vol. 355, No. 11 (Nov., 2003), pp. 4581-4594
Stable URL: http://www.jstor.org/stable/1194821
Page Count: 14
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Maximal Complexifications of Certain Homogeneous Riemannian Manifolds
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Abstract

Let M=G/K be a homogeneous Riemannian manifold with dim CG C=dim RG, 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 homogeneous Riemannian 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 neither holomorphically separable nor holomorphically convex.

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