Publication details
A New 1/2-Ricci Type Formula on the Spinor Bundle and Applications
| Authors | |
|---|---|
| Year of publication | 2017 |
| Type | Article in Periodical |
| Magazine / Source | Advances in Applied Clifford Algebras |
| Citation | |
| Web | https://doi.org/10.1007/s00006-017-0810-2 |
| 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 |
| Description | 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. |