Rotations and Hermitian symmetric spaces
type: Item
instance of: scholarly article
title: Rotations and Hermitian symmetric spaces
zbMATH Open document ID: 0712.53007
DOI: 10.1007/BF01320693
author: Lorenzo Nicolodi
author: Lieven Vanhecke
published in: Monatshefte für Mathematik
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178476
review text: On an almost Hermitian manifold (M,g,J) one considers the naturally defined field of local diffeomorphisms (J-rotations) \(j_ m=\exp_ m\circ J_ m\circ \exp_ m^{-1}\), \(m\in M\), and in particular, one studies isometric, harmonic, holomorphic and symplectic J-rotations. This leads to some characterizations of special classes of almost Hermitian manifolds, including the class of Hermitian symmetric spaces. In addition, one treats some properties of the shape operator (extrinsic geometry) and of the Ricci operator (intrinsic geometry) of a geodesic sphere relating to the J-rotations.
Mathematics Subject Classification ID: 53A15
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 4171863
zbMATH Keywords: almost Hermitian manifold
zbMATH Keywords: J-rotations
zbMATH Keywords: Hermitian symmetric spaces
zbMATH Keywords: shape operator
zbMATH Keywords: Ricci operator
zbMATH Keywords: geodesic sphere
reviewed by: Lieven Vanhecke
MaRDI profile type: Publication
cites work: Differential geometry of geodesic spheres.
cites work: Q3982336
cites work: Q3767955
cites work: A Report on Harmonic Maps
cites work: Riemannian manifolds with geodesic symmetries of order 3
cites work: Almost Hermitian manifolds with constant holomorphic sectional curvature
cites work: Generalized symmetric spaces
cites work: Symmetries and locally s-regular manifolds
cites work: SYMPLECTIC GEODESIC SYMMETRIES ON KÄHLER MANIFOLDS
cites work: Harmonic maps and $s$-regular manifolds
cites work: Q4155448
cites work: An example of a 6-dimensional flat almost Hermitian manifold
OpenAlex ID: W1995448825
description: scientific article; zbMATH DE number 4171863