Spinorial Representation of Submanifolds in Riemannian Space Forms

Abstract

In this paper we give a spinorial representation of submanifolds of any dimension and codimension into Riemannian space forms in terms of the existence of so called generalized Killing spinors. We then discuss several applications, among them a new and concise proof of the fundamental theorem of submanifold theory. We also recover results of T. Friedrich, B. Morel and the authors in dimension 2 and 3.

24 pages

References in corpus (2)

• Generalized Killing spinors and Lagrangian graphs
• Spinor representation of Lorentzian surfaces in R^{2,2}

Cited by in corpus (7)

• Spinorial representation of submanifolds in metric Lie groups
• Immersion in Sn by complex spinors
• Immersion in Rn by Complex irreducible Spinors
• Immersion in ${\mathbb{R}}^n$ by complex spinors
• Spinorial representation of surfaces in Lorentzian homogeneous spaces of dimension 3
• Spinorial representation of submanifolds in $S{L}_n(\mathbb{C})/SU(n)$
• Characterization of hypersurfaces in four dimensional product spaces via two different Spin${}^c$ structures