DOI QR코드

DOI QR Code

THE AXIOM OF INDEFINITE SURFACES IN SEMI-RIEMANNIAN MANIFOLDS

  • Received : 2011.08.29
  • Accepted : 2011.11.18
  • Published : 2011.11.30

Abstract

In this paper, we characterize a semi-Riemannian manifolds satisfies the axiom of indefinite surfaces. We obtain the following result: If a semi-Riemannian manifold satisfies the axiom of indefinite surfaces, then it is a real space form.

Keywords

References

  1. Cartan, E.: Lecons sur la geometrie des espaces de Riemann. Paris, Gauthiers-Villars, 1946.
  2. Duggal, K.L. & Bejancu, A.: Lightlike Submanifolds of Semi - Riemannian Manifolds and Applications. Kluwer Acad. Publishers, Dordrecht, 1996.
  3. Duggal, K.L. & Jin, D.H.: Totally umbilical lightlike submanifolds. Kodai Math. J. 26 (2003), 49-68. https://doi.org/10.2996/kmj/1050496648
  4. Graves, L. & Nomizu, K.: On sectional curvature of indefinite metric I. Math. Ann. 232 (1978), 267 - 272. https://doi.org/10.1007/BF01351431
  5. Kumar, R., Rani, R. & Nagaich, R.K.: The axiom of spheres in semi-Riemannian geometry with lightlike submanifolds. Kodai Math. J. 32 (2009), 52-58. https://doi.org/10.2996/kmj/1238594545
  6. Leung, D.S. & Nomizu, K.: The axiom of spheres in Riemannian geometry. J. Differential Geometry 5 (1971), 487 - 489. https://doi.org/10.4310/jdg/1214430010
  7. O'Neill, B.: Semi - Riemannian Geometry with Applications to Relativity. Academic Press, 1983.