Isometric, holomorphic and symplectic reflections
type: Item
instance of: scholarly article
title: Isometric, holomorphic and symplectic reflections
zbMATH Open document ID: 0673.53035
DOI: 10.1007/BF00572443
published in: Geometriae Dedicata
publication date: 1989-01-01T00:00:00Z
review text: The authors study local reflections in Riemannian, almost Hermitian and Kählerian manifolds with respect to topologically embedded submanifolds. The assumptions that these reflections are isometric, or holomorphic, or symplectic (or combinations of these assumptions) have a strong influence on the intrinsic and extrinsic geometry of the corresponding submanifolds. Typically, they are proved to be totally geodesic, or holomorphic, or having both properties, according to the situation. Some technical results in this paper (derived by the method of Jacobi vector fields) seem to be of interest for themselves and waiting for other applications.
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 4102033
zbMATH Keywords: almost Hermitian manifold
zbMATH Keywords: holomorphic map
zbMATH Keywords: symplectic map
zbMATH Keywords: isometry
zbMATH Keywords: symmetry
zbMATH Keywords: local reflections
zbMATH Keywords: Kählerian manifolds
zbMATH Keywords: submanifolds
author: Bang-Yen Chen
author: Lieven Vanhecke
reviewed by: Oldřich Kowalski
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4102033