Spinorial characterizations of surfaces into three-dimensional homogeneous manifolds

Julien Roth (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We give spinorial characterizations of isometrically immersed surfaces into three-dimensional homogeneous manifolds with four-dimensional isometry group in terms of the existence of a particular spinor field. This generalizes works by Friedrich for R(3) and Morel for S(3) and H(3). The main argument is the interpretation of the energy-momentum tensor of such a spinor field as the second fundamental form up to a tensor depending on the structure of the ambient space. (C) 2010 Elsevier B.V. All rights reserved.

Julien Roth. Spinorial characterizations of surfaces into three-dimensional homogeneous manifolds. Journal of Geometry and Physics, 2010, 60 (6-8), pp.1045--1061. ⟨10.1016/j.geomphys.2010.03.007⟩. ⟨hal-00693020⟩