Spinorial Representation of Surfaces into 4-dimensional Space Forms

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 ${\mathbb{R}}^3$ and in $S^3$ given by T. Friedrich and by B. Morel

21 pages

References in corpus (1)

• Surfaces in the four-space and the Davey--Stewartson equations

Cited by in corpus (1)

• On the spinorial representation of spacelike surfaces into 4-dimensional Minkowski space