The necessary and sufficient condition for the existence of alpha-surfaces in complex space-time manifolds with nonvanishing torsion is derived. For these manifolds, Lie brackets of vector fields and spinor Ricci identities contain explicitly the effects of torsion. This leads to an integrability condition for alpha-surfaces which does not involve just the self-dual Weyl spinor, as in complexified general relativity, but also the torsion spinor, in a nonlinear way, and its covariant derivative. A similar result also holds for four-dimensional, smooth real manifolds with a positive-definite metric. Interestingly, a particular solution of the integrability condition is given by right-flat and right-torsion-free space-times.
The geometry of complex space-times with torsion / Esposito, G. - (1993), pp. 481-483. (Intervento presentato al convegno 10th Italian Conference on General Relativity and Gravitational Physics tenutosi a Bardonecchia nel September 1992).
The geometry of complex space-times with torsion
ESPOSITO GPrimo
1993
Abstract
The necessary and sufficient condition for the existence of alpha-surfaces in complex space-time manifolds with nonvanishing torsion is derived. For these manifolds, Lie brackets of vector fields and spinor Ricci identities contain explicitly the effects of torsion. This leads to an integrability condition for alpha-surfaces which does not involve just the self-dual Weyl spinor, as in complexified general relativity, but also the torsion spinor, in a nonlinear way, and its covariant derivative. A similar result also holds for four-dimensional, smooth real manifolds with a positive-definite metric. Interestingly, a particular solution of the integrability condition is given by right-flat and right-torsion-free space-times.File | Dimensione | Formato | |
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