Symmetry and local conjugacy on complex manifolds
type: Item
instance of: scholarly article
title: Symmetry and local conjugacy on complex manifolds
zbMATH Open document ID: 0681.32023
DOI: 10.1007/BF01453579
author: Wilhelm Kaup
author: Jean-Pierre Vigué
published in: Mathematische Annalen
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164641
review text: The structure of the set S of all symmetric points in a complex manifold M with metric is studied (a\(\in M\) is called symmetric if a is isolated in the fixed point set of a biholomorphic isometry of M with period 2). In finite dimensions it is shown (actually for the bigger set of all pseudo-symmetric points) that S is a closed real-analytic submanifold of M and that any two points of a connected component of S are conjugate with respect to a biholomorphic isometry of M. In infinite dimensions counter-examples show that this result is not true in general. But it holds for the set of circular points.
reviewed by: Wilhelm Kaup
Mathematics Subject Classification ID: 32M15
Mathematics Subject Classification ID: 58B99
zbMATH DE Number: 4115000
zbMATH Keywords: finite dimension
zbMATH Keywords: infinite dimension
zbMATH Keywords: symmetric points
zbMATH Keywords: complex manifold
zbMATH Keywords: pseudo-symmetric points
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4115000