Spinorial characterizations of surfaces into 3-dimensional psuedo-Riemannian space forms

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Lawn, Marie-Amélie; Roth, Julien;
  • Publisher: Springer Verlag
  • Subject: [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] | 53C27, 53C40, 53C80, 58C40 | spineurs | Immersions isométriques | [ MATH.MATH-DG ] Mathematics [math]/Differential Geometry [math.DG]
    arxiv: General Relativity and Quantum Cosmology | Mathematics::Differential Geometry

9 pages; We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For Lorentzian surfaces, this generalizes a recent work of the first author in $\mathbb{R}^{2,1}$ to other Lorentzia... View more
  • References (10)

    [1] C. B¨ar, P. Gauduchon, and A. Moroianu, Generalized cylinders in semiRiemannian and spin geometry, Math. Z. 249 (2005), no. 3, 545580.

    [2] H. Baum, Spin-Strukturen und Dirac Operatoren u¨ber pseudoRiemannschen Mannigfaltgkeiten, Teubner-Texte zur Mathematik, Bd. 41 Teubner-Verlag, Leipzig, 1981.

    [3] H. Baum and O. Mu¨ller, Codazzi spinors and global ly hyperbolic manifolds with special holonomy, Math. Z. 258 (2008), no. 1, 185211.

    [4] T. Friedrich, On the spinor representation of surfaces in Euclidean 3-space, J. Geom. Phys. 28 (1998), 143157.

    [5] M.A. Lawn, A spinorial representation for lorentzian surfaces in R2,1 , J. Geom. Phys. 58 (2008) no. 6, 683-700.

    [6] M.A. Lawn, J. Roth, Isometric immersions of Hypersurfaces into 4- dimensional manifolds via spinors, to appear in Diff. Geom. Appl.

    [7] B. Lawson and M.-L. Michelson, Spin Geometry, Princeton University Press, 1989.

    [8] B. Morel, Surfaces in S3 and H3 via spinors, Actes du s´eminaire de th´eorie spectrale et g´eom´etrie, Institut Fourier, Grenoble 23 (2005), 922.

    [9] B. ONeill, Semi-riemannian geometry with applications to relativity, Academic Press, New York, 1983.

    [10] J. Roth, Spinorial characterizations of surfaces into 3-homogeneous manifolds, to appear in J. Geom. Phys.

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