Parallel spinors and basic holonomy in pseudo-Hermitian geometry
type: Item
instance of: scholarly article
title: Parallel spinors and basic holonomy in pseudo-Hermitian geometry
zbMATH Open document ID: 1423.32030
author: Felipe Leitner
published in: Annals of Global Analysis and Geometry
publication date: 2019-03-18T00:00:00Z
review text: The relationship between parallel sections in vector bundles and holonomy with respect to the Webster-Tanaka connection of pseudo-Hermitian geometry is studied. This is an interesting question in particular in the Cauchy-Riemann geometry setting. This connection can be regarded as a metric one with torsion. However, the behavior of its pseudo-Hermitian holonomy group is not completely natural and that is why the author endeavors in this paper to introduce an adjusted connection, called by the basic connection of pseudo-Hermitian geometry with corresponding basic holonomy group. Basic holonomy groups are suitable to describe pseudo-Einstein spaces and to consider the existence of parallel spinor fields. As one of the main results of this work, it is shown that the basic holonomy algebra of any pseudo-Einsten space is reduced to the special unitary algebra.
reviewed by: Masoud Sabzevari
Mathematics Subject Classification ID: 32V05
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 53C29
zbMATH DE Number: 7037383
zbMATH Keywords: CR geometry
zbMATH Keywords: pseudo-Einstein structures
zbMATH Keywords: holonomy
zbMATH Keywords: parallel spinors
MaRDI profile type: Publication
full work available at URL: s10455-018-9622-4
OpenAlex ID: W2884739598
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Wikidata QID: Q129500525
DOI: 10.1007/S10455-018-9622-4
description: scientific article; zbMATH DE number 7037383