Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/3341

 Title: Generalized Goldberg-Sachs Theorems for Pseudo-Riemannian Four-Manifolds Authors: Apostolov, Vestislav Keywords: Pseudo-Riemannian metricsHermitian GeometryGeneral RelativityDepartment of Complex Analysis Issue Date: Sep-1996 Publisher: Institute of Mathematics with Computer Center at the Bulgarian Academy of Sciences Citation: Preprint Series/Report no.: 1996;8 Abstract: It has been recently observed that the Generalized Goldberg-Sachs Theorem in General Relativity as well as some of its corollaries admit appropriate Riemannian versions. In this paper we use the formalism of spinors to give alternative proofs of these results clarifying the analogy between the positive Hermitian structures of oriented Riemannian four-manifolds and the shear-free congruences of oriented Lorentzian four-manifolds. We also prove similar results for the oriented pseudo-Rimennian four-manifolds when the metric is of zero signature. This allows us to describe the compact oriented four-manifolds possibly addmiting a pseudo-Riemannian Einstein metric of zero signature whose positive Weyl tensor has two distinctinct eigenvalues corresponding to non-isotropic eigenspaces.1991 MSC: 53C50; 53C55. Description: [Apostolov Vestislav; Апостолов Вестислав] URI: http://hdl.handle.net/10525/3341 Appears in Collections: Preprints

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