Surfaces in S³ and H³ via Spinors

2002/04/08 by Bertrand Morel, Morel, Bertrand · 1 citation
Mathematics · #53A10 #53C27 #53C45 #Advanced Operator Algebra Research #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.DG #msc:53A10 #msc:53C27 #msc:53C45

paper · pdf · doi:10.48550/arxiv.math/0204090

LaTeX, 12 pages

openalex publication_date 2002/04/08 · arxiv created 2003/02/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the spinorial characterization of isometric immersions of surfaces in R³ given by T. Friedrich (On the spinor representation of surfaces in Euclidean 3-space, J. Geom. Phys. 28 (1998)) to surfaces in S³ and H³. 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.

Cited by

• Characterization of hypersurfaces in four dimensional product spaces via two different Spin^c structures

Related

• The spinor and Weierstrass representations of surfaces in space
• Spinorial representation of submanifolds in a product of space forms
• The Spinor Representation of Surfaces in Space
• Finding Conformal and Isometric Immersions of Surfaces
• Immersion in ℝⁿ by complex spinors