Let M = G/K be a homogeneous Riemannian manifold with dim_C G^C = dim_R G, 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.

Halverscheid, S., Iannuzzi, A. (2003). Maximal complexifications of certain Riemannian homogeneous manifolds. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY [10.2307/1194821].

Maximal complexifications of certain Riemannian homogeneous manifolds.

IANNUZZI, ANDREA
2003-01-01

Abstract

Let M = G/K be a homogeneous Riemannian manifold with dim_C G^C = dim_R G, 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.
2003
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Con Impact Factor ISI
Adapted complex structure, homogeneous Riemannian spaces, Stein manifold.
Halverscheid, S., Iannuzzi, A. (2003). Maximal complexifications of certain Riemannian homogeneous manifolds. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY [10.2307/1194821].
Halverscheid, S; Iannuzzi, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/91907
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