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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.
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Submitted on : Thursday, February 11, 2016 - 9:46:40 AM
Last modification on : Tuesday, January 18, 2022 - 2:26:05 PM
Long-term archiving on: : Saturday, November 12, 2016 - 5:10:42 PM

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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⟩

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