Killing and twistor spinors with torsion

J 2016

Killing and twistor spinors with torsion

CHRYSIKOS, Ioannis

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

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

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

Abstract

V originále

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

Citovat

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.

@article{1380293,
   author = {Chrysikos, Ioannis},
   article_location = {Springer P.O. AH Dordrecht},
   article_number = {2},
   doi = {http://dx.doi.org/10.1007/s10455-015-9483-z},
   keywords = {Characteristic connection; Parallel spinor; Twistor spinor; Killing spinor with torsion; del-Einstein structure; Cubic Dirac operator},
   language = {eng},
   issn = {0232-704X},
   journal = {Annals of Global Analysis and Geometry},
   title = {Killing and twistor spinors with torsion},
   volume = {49},
   year = {2016}
}

TY  - JOUR
ID  - 1380293
AU  - Chrysikos, Ioannis
PY  - 2016
TI  - Killing and twistor spinors with torsion
JF  - Annals of Global Analysis and Geometry
VL  - 49
IS  - 2
SP  - 105-141
EP  - 105-141
PB  - Springer
SN  - 0232704X
KW  - Characteristic connection
KW  - Parallel spinor
KW  - Twistor spinor
KW  - Killing spinor with torsion
KW  - del-Einstein structure
KW  - Cubic Dirac operator
N2  - 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.
ER  -

CHRYSIKOS, Ioannis. Killing and twistor spinors with torsion. \textit{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.

Detailed Information on Publication Record