Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The intrinsic conformal structure and Gauss map of a light-like hypersurface in Minkowski space


Author: Marek Kossowski
Journal: Trans. Amer. Math. Soc. 316 (1989), 369-383
MSC: Primary 53C50; Secondary 53A30, 53C40
DOI: https://doi.org/10.1090/S0002-9947-1989-0938920-1
MathSciNet review: 938920
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We begin by pointing out two subtleties in the global properties of hypersurfaces in Minkowski space which inherit a uniformly degenerate metric (i.e., the existence of global space-like sections and the notion of an icon; see Appendices 1 and 2). We then construct a Gauss map for such hypersurfaces and an intrinsic invariant. This leads us to results concerning light-like hypersurfaces which parallel known results concerning surfaces in Euclidean space.


References [Enhancements On Off] (What's this?)

  • [B] J. K. Beem and P. E. Ehrlich, Global Lorentzian geometry, Dekker, 1981. MR 619853 (82i:53051)
  • [B] R. Bryant (personal communication).
  • 1. [K1 M. Kossowski, Fold singularities in pseudo-Riemannian geodesic tubes, Proc. Amer. Math. Soc. 95 (1985), 463-469. MR 806088 (87f:58023)
  • [K2] -, Pseudo-Riemannian metric singularities and the exlendability of parallel transport, Proc. Amer. Math. Soc. 99 (1987), 147-154. MR 866445 (88i:53104)
  • [K3] -, The $ {S^2}$-valued Gauss maps and split total curvature of a space-like codimension $ 2$ surface in Minkowski space (preprint).
  • [K4] -, A Gauss map and hybrid degree formula for compact hypersurfaces in Minkowski space (preprint).
  • [K5] -, Intersection in the space-like Grassmannian and the tilt of a space-like surface (preprint).
  • [ON] B. O'Neil, Semi Riemannian geometry with applications to relativity, Academic Press, New York, 1983. MR 719023 (85f:53002)
  • [P] R. Penrose, Battile recontates (DeWitt and Wheeler, ed.), Benjamin, New York, 1968.
  • [P] -, General relativity (O'Raifeartaigh, ed.), Clarendon Press, Oxford, 1972.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 53C50, 53A30, 53C40

Retrieve articles in all journals with MSC: 53C50, 53A30, 53C40


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1989-0938920-1
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society