Skip to main content
Log in

Fully stratified compact hypersurfaces in Minkowski 4-space

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

A compact hypersurface in Minkowski space decomposes as a disjoint union of loci where the induced metric is: definite, degenerate, or indefinite. Here we deduce several global properties of the hypersurface from properties of its degenerate loci.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Beem, J. and Ehrlich, P.,Global Lorentzian Geometry, Decker, New York, 1981.

    Google Scholar 

  2. Birman, G. and Nomizu, K., ‘The Gauss-Bonnet theorem for 2-dimensional spacetimes’,Mich. Math. J. 31 (1984).

  3. Chern, S. S., ‘Pseudo-Riemannian geometry and Gauss-Bonnet formula’,An. Acad. Brasil. Ci 35 (1963).

  4. Guillemin, V. and Golubitsky, M.,Stable Mappings and their Singularities; Grad. Texts in Math. 14, Springer, New York.

  5. Hirsch, M., Pugh, C. and Shub, M.,Invariant Manifolds; Lecture Notes in Math. 583, Springer-Verlag.

  6. Kossowski, M., ‘Pseudo Riemannian metric singularities and extendability of parallel transport’,Proc. Amer. Math. Soc. 99(1) (1989).

  7. Kossowski, M., ‘A Gauss map and hybrid degree formula for compact hypersurfaces in Minkowski space’,Geom. Dedicata 32 (1989).

  8. Kossowski, M., ‘TheS 2-valued Gauss maps and split total curvature of a space-like codimension-2 surface in Minkowski space’,J. London Math. Soc. 2, No. 2 (1989).

    Google Scholar 

  9. Kossowski, M., ‘The intrinsic conformal structure and Gauss map of a light-like hypersurface in Minkowski space’,Trans. Amer. Math. Soc. 316, No. 1 (1989).

    Google Scholar 

  10. Kossowski, M., ‘The total split curvatures of knotted space-like 2 spheres in Minkowski 4-space’ (to appear inProc. Amer. Math. Soc.).

  11. Kossowski, M., ‘The null blow up of a surface in Minkowski 3-space and intersection in the space-like Grassmann’,Mich. Math. J. 38 (1991).

  12. Kossowski, M., ‘The Lagrangian Gauss image for a compact surface in Minkowski 3-space’ (to appear inAnn. Global Anal. Geom.).

  13. Kossowski, M., ‘The Lagrangian Gauss image of a surface in Euclidean 3-space’ (to appear inProc. Amer. Math. Soc.).

  14. Kossowski, M., ‘Restrictions on zero mean curvature surfaces in Minkowski space’,Quart. J. Math. Oxford 42, No. 2 (1991).

    Google Scholar 

  15. Kossowski, M., ‘Prescribing invariants of Lagrangian surfaces’,Topology 31, No. 2 (1992).

  16. O'Neill, B.,Semi-Riemannian Geometry, Academic Press, 1963.

  17. Milnor, T. K., ‘Harmonic maps and classical surface theory in Minkowski 3-space’,Trans. Amer. Math. Soc. 280, No. 1 (1983).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research partially supported by NSF Grant DMS-88-03585.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kossowski, M. Fully stratified compact hypersurfaces in Minkowski 4-space. Geom Dedicata 47, 297–316 (1993). https://doi.org/10.1007/BF01263662

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01263662

Keywords

Navigation