Thickenings and conformal gravity
Remarking the important fact that the complex structure of an ambitwistor space completely encodes the conformal structure of the complex space- time, the author develops, in a very detailed way, a twistor correspondence for complex conformal space-times with vanishing Bach and Eastwood-Dighton tensors. In this manner, a reformulation of the conformally invariant aspects of Einstein's vacuum equations is performed by the use of the deformations of complex analytic spaces. One of the most important results, of this generalized technique in the analysis of complex conformal structures, arises when the Weyl curvature is algebraically general, because the equations which are obtained are precisely the conformal version of Einstein's vacuum equations with cosmological constant. This result represents a completely curved version of the linearized correspondence conjectured first by \textit{R. J. Baston} and \textit{L. J. Mason} [Classical Quantum Gravity 4, No.4, 815-826 (1987; Zbl 0647.53057)]. At the end the author describes relations between this work and conformal supergravity, which suggests the use of the complex supermanifolds, and also points out a number of future directions for extending the present results.
scientific article; zbMATH DE number 4212961
scientific article