Advanced Search

We generalize the spinorial characterization of isometric immersions of surfaces in ${ℝ}^3$ given by T. Friedrich to surfaces in ${𝕊}^3$ and ${ℍ}^3$. The main argument is the interpretation of the energy-momentum tensor associated with a special spinor field as a second fundamental form. It turns out that such a characterization of isometric immersions in terms of a special section of the spinor bundle also holds in the case of hypersurfaces in the Euclidean $4$-space.