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ON ODD-DIMENSIONAL COMPLEX ANALYTIC KLEINIAN GROUPS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 108 / Issue 1 / February 2020
- Published online by Cambridge University Press:
- 12 February 2019, pp. 1-32
- Print publication:
- February 2020
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- Article
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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.
