Spinorial characterizations of surfaces into 3-dimensional psuedo-Riemannian space forms

Marie-Amélie Lawn (1) , Julien Roth (2)

1 Unité de recherche en mathématiques
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For Lorentzian surfaces, this generalizes a recent work of the first author in $\mathbb{R}^{2,1}$ to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well as for spacelike and timelike immersions of surfaces of signature (0,2), hence achieving a complete spinorial description for this class of pseudo-Riemannian immersions.

Mots clés: Immersions isométriques; spineurs

Domaines: Géométrie différentielle [math.DG]

Marie-Amélie Lawn, Julien Roth. Spinorial characterizations of surfaces into 3-dimensional psuedo-Riemannian space forms. Mathematical Physics, Analysis and Geometry, 2011, 14 (3), pp.185-195. ⟨hal-00450968⟩