Immersions of Lorentzian surfaces in R2,1

JOURNAL OF GEOMETRY AND PHYSICS

卷:58

Article

Lawn, Marie-Amelie

关键词: Dirac operator;    Lorentzian surfaces;    isometric and conformal immersions;    Gauss and Codazzi equations;   

DOI  :  10.1016/j.geomphys.2008.01.007

来源: Elsevier

【 摘 要 】

We study whether a given Lorentzian surface (M, g) can be immersed as the hypersurface of codimension one into the pseudo-Euclidean space R-2,R-1. Using the methods of para-complex geometry and real spinor representations we succeed in proving the equivalence between the data of a spacelike conformal immersion of (M, g) into R-2,R-1 and two spinors satisfying a Dirac-type equation on the surface. We generalize in this way with new technics a result of Friedrich [Th. Friedrich, On the spinor representation of surfaces in euclidean 3-Space, J. Geom. Phys. 28 (1-2) (1998) 143-157] to the pseudo-Riemannian context. Moreover we give a geometrically invariant representation of such surfaces using two Dirac spinors. (c) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free