Spinorial characterizations of Surfaces into 3-dimensional homogeneous Manifolds
نویسنده
چکیده
We give a spinorial characterization of isometrically immersed surfaces into 3-dimensional homogeneous manifolds with 4-dimensional isometry group in terms of the existence of a particular spinor, called generalized Killing spinor. This generalizes results by T. Friedrich [7] for R3 and B. Morel [16] for S3 and H3. The main argument is the interpretation of the energy-momentum tensor of a genralized Killing spinor as the second fondamental form up to a tensor depending on the structure of the ambient space. keywords: Dirac Operator, Killing Spinors, Isometric Immersions, Gauss and Codazzi Equations. subjclass: Differential Geometry, Global Analysis, 53C27, 53C40, 53C80, 58C40.
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