Conformal nonlinear graviton

Abstract

2. Let M be a four-dimensional complex manifold in which two holomorphic locally free spinor bundles S and S of rank 2 are given, together with the following identities: TM = S ® S, where TM is a tangent bundle and A2S = A2S. These identities define a holomorphic conformal structure in M, i.e., an invertible subbundle C ®2 in ~IM ® ~IM, where the symbol ® denotes the symmetric tensor product and C: = A=S *.