Peter Dalakov and Stefan Ivanov 2001 Class. Quantum Grav. 18 253 doi:10.1088/0264-9381/18/2/305
Harmonic spinors of the Dirac operator of connection with torsion in dimension four
Peter Dalakov1 and Stefan Ivanov2
Show affiliationsIt is shown that the existence of a parallel (-)-spinor with respect to a metric connection with totally skew-symmetric torsion requires more local restrictions than the existence of a parallel (+)-spinor. It is proved that every harmonic spinor with respect to the Dirac operator of this connection on a compact four-dimensional spin Riemannian manifold is parallel with respect to a naturally arising metric connection with totally skew-symmetric torsion and all such spaces are classified up to a conformal transformation.
- PACS
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04.20.Gz Spacetime topology, causal structure, spinor structure
- MSC
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58D17 Manifolds of metrics (esp. Riemannian)
83C60 Spinor and twistor methods; Newman-Penrose formalism
15A66 Clifford algebras, spinors
34L40 Particular operators (Dirac, one-dimensional Schrödinger, etc.)
- Subjects
- Dates
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Issue 2 (21 January 2001)
Received 23 June 2000
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Harmonic spinors of the Dirac operator of connection with torsion in dimension four
Peter Dalakov and Stefan Ivanov 2001 Class. Quantum Grav. 18 253
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