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ON ODD-DIMENSIONAL COMPLEX ANALYTIC KLEINIAN GROUPS

Part of: Compact analytic spaces Geometric convexity Riemann surfaces Global differential geometry

Published online by Cambridge University Press:  12 February 2019

MASAHIDE KATO
MASAHIDE KATO*
Affiliation:
Sophia University, Kioicho 7-1, Chiyoda-ku, Tokyo 102-8554, Japan email [email protected]
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Abstract

We shall explain here an idea to generalize classical complex analytic Kleinian group theory to any odd-dimensional cases. For a certain class of discrete subgroups of $\text{PGL}_{2n+1}(\mathbf{C})$ acting on $\mathbf{P}^{2n+1}$, we can define their domains of discontinuity in a canonical manner, regarding an $n$-dimensional projective linear subspace in $\mathbf{P}^{2n+1}$ as a point, like a point in the classical one-dimensional case. Many interesting (compact) non-Kähler manifolds appear systematically as the canonical quotients of the domains. In the last section, we shall give some examples.

Keywords

compact non-Kähler manifoldprojective structureKleinian group theory

MSC classification

Primary: 32J18: Compact $n$-folds
Secondary: 30F40: Kleinian groups 32F10: $q$-convexity, $q$-concavity 32F17: Other notions of convexity 53C56: Other complex differential geometry
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 108 , Issue 1 , February 2020 , pp. 1 - 32
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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