The length function of a twistor spinor with zero
type: Item
instance of: scholarly article
title: The length function of a twistor spinor with zero
zbMATH Open document ID: 1263.53042
author: Fatmagül Mintaş
published in: Annals of Global Analysis and Geometry
publication date: 2012-03-23T00:00:00Z
review text: Let \((M^n , g)\), be an \(n\)-dimensional Riemannian spin manifold and \(\Sigma M\) its spinor bundle. Let \(\nabla^\Sigma\) and \(D\) denote the spinor derivative and the Dirac operator on \(M^n\) respectively. A spinor field \(\Phi\) is called a twistor spinor if it satisfies the equation \(\nabla^\Sigma_X\Phi + \frac1n X.D \Phi = 0\), for all vectors fields \(X\) on \(M\), where \(.\) denotes the Clifford multiplication defined by the spinor representation. Such an equation is called the twistor equation. The paper under review is a presentation of important facts concerning the Taylor expansion of the length function of a twistor spinor with zero on a Riemannian orbifold around its zero. The author gives a thorough study on the Eguchi-Hanson orbifold. The expansion is written by using some conformal normal coordinates, briefly called \((CNC)\), around the zero up to order 7. In the example of the Eguchi-Hanson orbifold, the conformal normal coordinates \((CNC)\) are given explicitly. The author uses the expansion for computing the mass, a generalization of \((ADM)\)-mass, of the asymptotically locally Euclidean coordinate system, which is constructed from a conformal normal coordinate system around the zero of a twistor spinor on a Riemannian spin orbifold admitting isolated singularities.
reviewed by: Pierre Anglès
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 53B20
Mathematics Subject Classification ID: 53B50
zbMATH DE Number: 6018064
zbMATH Keywords: twistor spinor
zbMATH Keywords: spin orbifold
zbMATH Keywords: ALE manifold
zbMATH Keywords: Eguchi-Hanson manifold
zbMATH Keywords: mass
MaRDI profile type: Publication
full work available at URL: s10455-011-9296-7
OpenAlex ID: W2057107823
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DOI: 10.1007/S10455-011-9296-7
description: scientific article; zbMATH DE number 6018064