Killing and twistor spinors with torsion

J 2016

Killing and twistor spinors with torsion

CHRYSIKOS, Ioannis

Základní údaje

Originální název

Killing and twistor spinors with torsion

Autoři

CHRYSIKOS, Ioannis (300 Řecko, garant, domácí)

Vydání

Annals of Global Analysis and Geometry, Springer P.O. AH Dordrecht, Springer, 2016, 0232-704X

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Nizozemské království

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 0.713

Kód RIV

RIV/00216224:14310/16:00094233

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1007/s10455-015-9483-z

UT WoS

000371236200001

Klíčová slova anglicky

Characteristic connection; Parallel spinor; Twistor spinor; Killing spinor with torsion; del-Einstein structure; Cubic Dirac operator

Štítky

AKR, rivok

Změněno: 11. 5. 2017 18:19, Ing. Andrea Mikešková

Anotace

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.

Návaznosti

GP14-24642P, projekt VaV

Název: Diracovy operátory s torzí a speciální geometrické struktury

Investor: Grantová agentura ČR, Diracovy operátory s torzí a speciální geometrické struktury

Citovat

CHRYSIKOS, Ioannis. Killing and twistor spinors with torsion. Annals of Global Analysis and Geometry. Springer P.O. AH Dordrecht: Springer, 2016, roč. 49, č. 2, s. 105-141. ISSN 0232-704X. Dostupné z: 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, roč.~49, č.~2, s.~105-141. ISSN~0232-704X. Dostupné z: https://dx.doi.org/10.1007/s10455-015-9483-z.

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