SPINORIAL REPRESENTATION OF SUBMANIFOLDS IN RIEMANNIAN SPACE FORMS

Pierre Bayard (1) , Marie-Amélie Lawn (2) , Julien Roth (3)

1 UNAM - Universidad Nacional Autónoma de México = National Autonomous University of Mexico
2 Department of Mathematics [Imperial College London]
3 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Mots clés: Spin geometry; Isometric Immersions; Weierstrass Representation

Domaines: Géométrie différentielle [math.DG]

Pierre Bayard, Marie-Amélie Lawn, Julien Roth. SPINORIAL REPRESENTATION OF SUBMANIFOLDS IN RIEMANNIAN SPACE FORMS. Pacific Journal of Mathematics, 2017, 291 (1), pp.51-80. ⟨hal-01272564⟩