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# Spinorial Characterization of Surfaces into 3-dimensional homogeneous Manifolds

Abstract : 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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https://hal.archives-ouvertes.fr/hal-00156448
Contributor : Julien Roth Connect in order to contact the contributor
Submitted on : Thursday, June 21, 2007 - 11:00:30 AM
Last modification on : Friday, July 9, 2021 - 11:30:42 AM
Long-term archiving on: : Thursday, April 8, 2010 - 8:58:08 PM

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characterization2.pdf
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### Identifiers

• HAL Id : hal-00156448, version 1
• ARXIV : 0706.3107

### Citation

Julien Roth. Spinorial Characterization of Surfaces into 3-dimensional homogeneous Manifolds. Journal of Geometry and Physics, Elsevier, 2010, 60 (6-8), pp.1045-1061. ⟨hal-00156448⟩

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