Holomorphic retractions of bounded symmetric domains onto totally geodesic complex submanifolds
type: Item
instance of: scholarly article
title: Holomorphic retractions of bounded symmetric domains onto totally geodesic complex submanifolds
author: Ngaiming Mok
published in: Chinese Annals of Mathematics. Series B
publication date: 2022-12-08T00:00:00Z
review text: This paper is a contribution to the geometry of bounded symmetric domains. The main result is as follows: Let \(\Omega \subset \mathbb{C}^n\) be such a domain, and \(G\) the identity component of the holomorphic automorphisms of \(\Omega \). Let \(E\subset \mathbb{C}^n\) be a complex vector subspace such that \(S=E\cap \Omega\) is a totally geodesic complex submanifold with respect to a \(G\)-invariant Kähler metric. Then \(\rho (\Omega )=S\), where \(\rho \) is the orthogonal projection \(\mathbb{C}^n\to E\). A special case has been considered previously by Yeung. In that case \(\Omega \) is the irreducible bounded symmetric domain in the space of symmetric complex matrices and \(S\) is isomorphic to the unit ball in the space \(M(a,b;\mathbb{C})\) of \(a\times b\) complex matrices. Furthermore the totally geodesic complex submanifolds in \(\Omega \) are characterized in terms of Jordan triple systems. The author gives also a characterization of the Harish-Chandra realization of bounded symmetric domains in terms of bisectional curvatures.
Mathematics Subject Classification ID: 32M15
Mathematics Subject Classification ID: 32H02
zbMATH DE Number: 7629821
zbMATH Keywords: bounded symmetric domain
zbMATH Keywords: totally geodesic
reviewed by: Jacques Faraut
MaRDI profile type: Publication
full work available at URL: s11401-022-0380-z
OpenAlex ID: W4310860990
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DOI: 10.1007/S11401-022-0380-Z
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description: scientific article; zbMATH DE number 7629821