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@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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