Spinorial Representation of Surfaces into 4-dimensional Space Forms

TL;DR

This paper introduces a spinorial method to represent surfaces in four-dimensional space forms, generalizing classical formulas and unifying characterizations in lower dimensions.

Contribution

It provides a new, geometrically invariant spinorial representation for surfaces in 4D space forms, extending known formulas and characterizations.

Findings

Derived a generalized Weierstrass representation for 4D surfaces

Unified spinorial characterizations of surfaces in D and S^3

Established a new invariant geometric framework

Abstract

In this paper we give a geometrically invariant spinorial representation of surfaces in four-dimensional space forms. In the Euclidean space, we obtain a representation formula which generalizes the Weierstrass representation formula of minimal surfaces. We also obtain as particular cases the spinorial characterizations of surfaces in $\R^3$ and in $S^3$ given by T. Friedrich and by B. Morel