Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-21T12:54:40.705Z Has data issue: false hasContentIssue false
  • English
  • Français

Conformally Flat Riemannian Manifolds as Hypersurfaces of the Light Cone

Part of: Global differential geometry Classical differential geometry

Published online by Cambridge University Press:  20 November 2018

A. C. Asperti  and
M. Dajczer
A. C. Asperti
Affiliation:
Antonio Carlos Asperti IME - USP C.P. 20570 (Agência Iguatemi) 01498 - São Paulo - Brasil
M. Dajczer
Affiliation:
Marcos Dajczer IMPA Estrada D. Castorina, 110 22460-Rio de Janeiro - Brasil
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Simply connected conformally flat Riemannian manifolds are characterized as hypersurfaces in the light cone of a standard flat Lorentzian space, transversal to its generators. Some applications of this fact are given.

MSC classification

Secondary: 53A30: Conformal differential geometry 53C40: Global submanifolds
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 3 , 01 September 1989 , pp. 281 - 285
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Brinkmann, W. H., On Riemannian spaces conformai to Euclidean space, Proc. Nat. Acad. Sci. USA 9 (1923), 1–3.Google Scholar
2. Eisenhart, L. P., Riemannian Geometry, Princeton University Press, Princeton, NJ, 1966.Google Scholar
3. Kuiper, N. H., On conformally flat spaces in the large, Annals of Mathematics 50, 1949, 916–924.Google Scholar
4. Kulkarni, R. S., Curvature and metric, Annals of Mathematics 91 (1970), 311–331.Google Scholar
5. O'Neill, B., Semi-Riemannian Geometry, Academic Press Inc., New York, 1983.Google Scholar
6. Ryan, P. J., Conformally flat spaces with constant scalar curvature, Proc. 13th biennial seminar of the Canadian Math. Congress, Halifax (1971), 115-124.Google Scholar
7. Schouten, J. A., Ûber die konforme Abbildung n-dimensionaler Mannigfaltigkeiten mit quadratischer Mafibestimmung auf eine Mannigfaltigkeit mit euklidischer Mafibestimmung, Math. Z. 11 (1921), 58–88.Google Scholar
8. Spivak, M., A Comprehensive Introduction to Differential Geometry, Vol. IV, Publish or Perish Inc., Berkeley (1979).Google Scholar
9. Weber, W. C. and Goldberg, S. I., Conformai deformations of Riemannian manifolds, Queen's papers on Pure and Applied Math. 16, Kingston (1969).Google Scholar