A New 1/2-Ricci Type Formula on the Spinor Bundle and
Applications

J 2017

A New 1/2-Ricci Type Formula on the Spinor Bundle and Applications

CHRYSIKOS, Ioannis

Základní údaje

Originální název

A New 1/2-Ricci Type Formula on the Spinor Bundle and Applications

Autoři

CHRYSIKOS, Ioannis

Vydání

Advances in Applied Clifford Algebras, Springer, 2017, 0188-7009

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Itálie

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.174

DOI

http://dx.doi.org/10.1007/s00006-017-0810-2

UT WoS

000414140500010

Klíčová slova anglicky

Characteristic connection; Dirac operator with torsion; Generalized Schrodinger-Lichnerowicz formula; 1/2-Ricci formula; Parallel spinors; Twistor spinors with torsion

Štítky

RIV ne

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 26. 5. 2023 11:56, Mgr. Marie Šípková, DiS.

Anotace

V originále

Consider a Riemannian spin manifold endowed with a non-trivial 3-form , such that , where is the metric connection with skew-torsion T. In this note we introduce a generalized -Ricci type formula for the spinorial action of the Ricci endomorphism , induced by the one-parameter family of metric connections . This new identity extends a result described by Th. Friedrich and E. C. Kim, about the action of the Riemannian Ricci endomorphism on spinor fields, and allows us to present a series of applications. For example, we describe a new alternative proof of the generalized Schrodinger-Lichnerowicz formula related to the square of the Dirac operator , induced by , under the condition . In the same case, we provide integrability conditions for -parallel spinors, -parallel spinors and twistor spinors with torsion. We illustrate our conclusions for some non-integrable structures satisfying our assumptions, e.g. Sasakian manifolds, nearly Kahler manifolds and nearly parallel -manifolds, in dimensions 5, 6 and 7, respectively.

Citovat

CHRYSIKOS, Ioannis. A New 1/2-Ricci Type Formula on the Spinor Bundle and Applications. Advances in Applied Clifford Algebras. Springer, 2017, roč. 27, č. 4, s. 3097-3127. ISSN 0188-7009. Dostupné z: https://dx.doi.org/10.1007/s00006-017-0810-2.

@article{2285883,
   author = {Chrysikos, Ioannis},
   article_number = {4},
   doi = {http://dx.doi.org/10.1007/s00006-017-0810-2},
   keywords = {Characteristic connection; Dirac operator with torsion; Generalized Schrodinger-Lichnerowicz formula; 1/2-Ricci formula; Parallel spinors; Twistor spinors with torsion},
   language = {eng},
   issn = {0188-7009},
   journal = {Advances in Applied Clifford Algebras},
   note = {Nevykazovat pro RIV. Afiliace autora je mimo MU.},
   title = {A New 1/2-Ricci Type Formula on the Spinor Bundle and Applications},
   url = {https://doi.org/10.1007/s00006-017-0810-2},
   volume = {27},
   year = {2017}
}

TY  - JOUR
ID  - 2285883
AU  - Chrysikos, Ioannis
PY  - 2017
TI  - A New 1/2-Ricci Type Formula on the Spinor Bundle and Applications
JF  - Advances in Applied Clifford Algebras
VL  - 27
IS  - 4
SP  - 3097-3127
EP  - 3097-3127
PB  - Springer
SN  - 01887009
N1  - Nevykazovat pro RIV. Afiliace autora je mimo MU.
KW  - Characteristic connection
KW  - Dirac operator with torsion
KW  - Generalized Schrodinger-Lichnerowicz formula
KW  - 1/2-Ricci formula
KW  - Parallel spinors
KW  - Twistor spinors with torsion
UR  - https://doi.org/10.1007/s00006-017-0810-2
N2  - Consider a Riemannian spin manifold endowed with a non-trivial 3-form , such that , where is the metric connection with skew-torsion T. In this note we introduce a generalized -Ricci type formula for the spinorial action of the Ricci endomorphism , induced by the one-parameter family of metric connections . This new identity extends a result described by Th. Friedrich and E. C. Kim, about the action of the Riemannian Ricci endomorphism on spinor fields, and allows us to present a series of applications. For example, we describe a new alternative proof of the generalized Schrodinger-Lichnerowicz formula related to the square of the Dirac operator , induced by , under the condition . In the same case, we provide integrability conditions for -parallel spinors, -parallel spinors and twistor spinors with torsion. We illustrate our conclusions for some non-integrable structures satisfying our assumptions, e.g. Sasakian manifolds, nearly Kahler manifolds and nearly parallel -manifolds, in dimensions 5, 6 and 7, respectively.
ER  -

CHRYSIKOS, Ioannis. A New 1/2-Ricci Type Formula on the Spinor Bundle and Applications. \textit{Advances in Applied Clifford Algebras}. Springer, 2017, roč.~27, č.~4, s.~3097-3127. ISSN~0188-7009. Dostupné z: https://dx.doi.org/10.1007/s00006-017-0810-2.

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