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On the Kobayashi Pseudometric Reduction of Homogeneous Spaces

Published online by Cambridge University Press:  20 November 2018

Bruce Gilligan
Bruce Gilligan*
Affiliation:
Department of Mathematics and Statistics, University of Regina Regina, Saskatchewan CanadaS4S 0A2
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Abstract

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Given any homogeneous complex manifold X = G/H, there exists a natural coset map π :G/H → G/K satisfying π (X1) = π (x2) if and only if dx(x1 x2) = 0, where dx denotes the Kobayashi pseudometric on X. Its typical fiber Z : = K/H is a connected complex submanifold of X. Also G/K has a (7-invariant complex structure, provided K satisfies a certain technical assumption (see Theorem 3). If Z is compact as well, then G/K is biholomorphic to a homogeneous bounded domain.

Keywords

32M1032H15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 1 , 01 March 1988 , pp. 45 - 51
Copyright
Copyright © Canadian Mathematical Society 1988

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