Killing and twistor spinors with torsion

CHRYSIKOS, Ioannis. Killing and twistor spinors with torsion. Annals of Global Analysis and Geometry. Springer P.O. AH Dordrecht: Springer, 2016, vol. 49, No 2, p. 105-141. ISSN 0232-704X. Available from: https://dx.doi.org/10.1007/s10455-015-9483-z.

Basic information

• Original name: Killing and twistor spinors with torsion
• Authors: CHRYSIKOS, Ioannis (300 Greece, guarantor, belonging to the institution).
• Edition: Annals of Global Analysis and Geometry, Springer P.O. AH Dordrecht, Springer, 2016, 0232-704X.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: Netherlands
• Confidentiality degree: is not subject to a state or trade secret
• Impact factor: Impact factor: 0.713
• RIV identification code: RIV/00216224:14310/16:00094233
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.1007/s10455-015-9483-z
• UT WoS: 000371236200001
• Keywords in English: Characteristic connection; Parallel spinor; Twistor spinor; Killing spinor with torsion; del-Einstein structure; Cubic Dirac operator
• Tags: AKR, rivok

Abstract

We study twistor spinors (with torsion) on Riemannian spin manifolds carrying metric connections with totally skew-symmetric torsion. We consider the characteristic connection and under the condition , we show that the twistor equation with torsion w.r.t. the family can be viewed as a parallelism condition under a suitable connection on the bundle , where is the associated spinor bundle. Consequently, we prove that a twistor spinor with torsion has isolated zero points. Next we study a special class of twistor spinors with torsion, namely these which are T-eigenspinors and parallel under the characteristic connection; we show that the existence of such a spinor for some implies that is both Einstein and -Einstein, in particular the equation holds for any . In fact, for -parallel spinors we provide a correspondence between the Killing spinor equation with torsion and the Riemannian Killing spinor equation. This allows us to describe 1-parameter families of non-trivial Killing spinors with torsion on nearly Kahler manifolds and nearly parallel -manifolds, in dimensions 6 and 7, respectively, but also on the 3-dimensional sphere . We finally present applications related to the universal and twistorial eigenvalue estimate of the square of the cubic Dirac operator.

Links

• GP14-24642P, research and development project: Name: Diracovy operátory s torzí a speciální geometrické struktury

Investor: Czech Science Foundation