Pseudo-Hermitian symmetries
type: Item
instance of: scholarly article
title: Pseudo-Hermitian symmetries
zbMATH Open document ID: 1154.53016
author: Eric Boeckx
author: Jong Taek Cho
published in: Israel Journal of Mathematics
publication date: 2008-10-16T00:00:00Z
review text: Let \((M,\eta, J, g)\) be a strictly pseudo-convex CR manifold with a contact form \(\eta\), complex structure \(J\) on \(D = ker (\eta)\) and the Riemannian metric \[ g := \eta \otimes \eta + d \eta(J \cdot, \cdot)| _{D}. \] The authors say that this manifold is a Tanaka-Webster parallel space if the Tanaka-Webster connection \(\tilde \nabla\) has \(\tilde \nabla\)-parallel curvature \(\tilde R\) and torsion \(\tilde T\) tensors. The manifold \(M\) is called a weakly locally pseudo-Hermitian symmetric space if \[ g(\tilde \nabla_X \tilde R(Y,Z)U,V) =0 \] for all \(X,Y,Z,U,V \in D\). The authors give a description of Tanaka-Webster parallel spaces and weakly locally pseudo-Hermitian spaces. In particular, they prove that a Sasakian manifold is a locally pseudo-Hermitian symmetric space if and only if it is a locally Sasakian \(\varphi\)-symmetric space in the sense of Takahashi.
reviewed by: Dmitri Alekseevsky
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53D10
zbMATH DE Number: 5351776
zbMATH Keywords: metric contact structures
zbMATH Keywords: CR structures
zbMATH Keywords: Tanaka-Webster connection
zbMATH Keywords: Sasakian \(\varphi\)-symmetric spaces
zbMATH Keywords: generalized symmetric spaces
MaRDI profile type: Publication
full work available at URL: s11856-008-1023-0
OpenAlex ID: W2084460352
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DOI: 10.1007/S11856-008-1023-0
description: scientific article; zbMATH DE number 5351776