Spinorial representation of submanifolds in Riemannian space forms

Pierre Bayard, Marie-Amélie Lawn and Julien Roth

Vol. 291 (2017), No. 1, 51–80

DOI: 10.2140/pjm.2017.291.51

Abstract

We give a spinorial representation of submanifolds of any dimension and codimension into Riemannian space forms in terms of the existence of generalized Killing spinors. We 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 dimensions 2 and 3.

Keywords

Spin geometry, isometric immersions, Weierstrass representation

Mathematical Subject Classification 2010

Primary: 53C27, 53C40

Milestones

Received: 23 May 2016

Revised: 7 February 2017

Accepted: 10 March 2017

Published: 20 August 2017