Spinorial Characterization of Surfaces into 3-dimensional homogeneous Manifolds

Details Spinorial Characterization of Surfaces into 3-dimensional homogeneous Manifolds Spinorial Characterization of Surfaces into 3-dimensional homogeneous Manifolds

2007-06-21

arxiv.org/abs/0706.3107v1

Journal of Geometry and Physics 60, 6-8 (2010) 1045-1061

Mathematics

Differential Geometry

35 pages

Scientific paper

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 for $\R^3$ and B. Morel for $\Ss^3$ and $\HH^3$. 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

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