Spinorial representation of surfaces in four-dimensional Space Forms

Pierre Bayard (1) , Marie-Amélie Lawn (2) , Julien Roth (3)

1 Instituto de Fisica y Matematicas
2 Department of Mathematics and Statistics [Texas Tech]
3 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Mots clés: Dirac Operator; Isometric Immersions; Weierstrass Representation

Domaines: Géométrie différentielle [math.DG]

Pierre Bayard, Marie-Amélie Lawn, Julien Roth. Spinorial representation of surfaces in four-dimensional Space Forms. Annals of Global Analysis and Geometry, 2013, 44 (4), pp.433-453. ⟨hal-00807496⟩