Spinorial representation of submanifolds in a product of space forms

2022/06/02 by Basilio, Alicia, Bayard, Pierre, Lawn, Marie-Amélie +1
#53C27 #53C40 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.00956

Abstract

We present a method giving a spinorial characterization of an immersion in a product of spaces of constant curvature. As a first application we obtain a proof using spinors of the fundamental theorem of immersion theory in that spaces. We also study special cases: we recover previously known results concerning immersions in \mathbbS²×ℝ and we obtain new spinorial characterizations of immersions in \mathbbS²×ℝ² and in ℍ²×ℝ. We then study the theory of H=1/2 surfaces in ℍ²×ℝ using this spinorial approach, obtain new proofs of some of its fundamental results and give a direct relation with the theory of H=1/2 surfaces in ℝ^1,2.

Related

• Surfaces in S³ and H³ via Spinors
• Spinorial representation of submanifolds in SL_n(ℂ)/SU(n)
• The spinor and Weierstrass representations of surfaces in space
• The Spinor Representation of Surfaces in Space
• Immersion in Sn by complex spinors