The energy-momentum tensor on low dimensional \(\mathrm{Spin}^c\) manifolds
type: Item
instance of: scholarly article
zbMATH Open document ID: 1253.53049
DOI: 10.1142/S0129167X12500905
author: Georges Habib
author: Roger Nakad
published in: International Journal of Mathematics
publication date: 2012-09-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/1204.0541
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C80
zbMATH DE Number: 6078195
zbMATH Keywords: \(\mathrm{Spin}^c\) structures
zbMATH Keywords: Dirac operator
zbMATH Keywords: energy-momentum tensor
zbMATH Keywords: compact surfaces
zbMATH Keywords: low-dimensional \(\mathrm{Spin}^c\) manifolds
MaRDI profile type: Publication
arXiv ID: 1204.0541
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OpenAlex ID: W2135547899
Wikidata QID: Q125906001
title: The energy-momentum tensor on low dimensional \(\mathrm{Spin}^c\) manifolds
review text: The authors investigate the energy-momentum tensor on low-dimensional compact manifolds having an arbitrary \(\mathrm{Spin}^c\) structure. Their principal result is a new proof of a Bär-type inequality for the eigenvalues of the Dirac operator, and it is shown that the round sphere \(\mathbb{S}^2\) with its canonical \(\mathrm{Spin}^2\) structure satisfies this limiting case. They conclude by giving a spinorial chacterization of immersed surfaces in \(\mathbb{S}^2\times\mathbb{R}\), using solutions of the generalized Killing spinor equation associated with the induced \(\mathrm{Spin}^c\) structure on \(\mathbb{S}^2\times\mathbb{R}\).NEWLINENEWLINE Contents includes: An Introduction (containing a survey of the previous literature and a summary of their new results); Preliminaries (concerning \(\mathrm{Spin}^c\) structures and the Dirac operator); The two-dimensional case; The three-dimensional case; Characterization of surfaces in \(\mathbb S^2\times\mathbb R\).
reviewed by: Joseph D. Zund
description: scientific article; zbMATH DE number 6078195