Spinorial characterizations of surfaces into three-dimensional homogeneous manifolds

Abstract

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.