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@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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