A Non-holomorphic Penrose Transform forHyperbolic 3-Space

[[abstract]]The non-holomorphic Penrose transform is a generalization of the holomor-phic Penrose transform that was best examplified in [3], by the introduction ofinvolutive structure into the context, cf. [5]. In this paper, we apply the non-holomorphic Penrose transform to a non-holomorphic twistor correspondencefor hyperbolic 3-space. By considering every space of the correspondence asa homogeneous space for SL(2, C) and using the homogeneous type of thenon-holomorphic Penrose transform, we obtain more results on this case thanthat was presented in [2]