JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Maximal Hypersurfaces of (m + 2)-Dimensional Lorentzian Space Forms
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 48, Issue 1,  2008, pp.109-121
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2008.48.1.109
 Title & Authors
Maximal Hypersurfaces of (m + 2)-Dimensional Lorentzian Space Forms
Dursun, Ugur;
  PDF(new window)
 Abstract
We determine maximal space-like hypersurfaces which are the images of subbundles of the normal bundle of m-dimensional totally geodesic space-like submanifolds of an (m + 2)-dimensional Lorentzian space form (c) under the normal exponential map. Then we construct examples of maximal space-like hypersurfaces of (c).
 Keywords
Maximal hypersurface;space-like submanifold;mean curvature;Lorentzian space form;
 Language
English
 Cited by
 References
1.
K. Akutagawa, On space-like hypersurfaces with constant mean curvature in the de Sitter space, Math. Z., 196(1)(1987), 13-19. crossref(new window)

2.
L. J. Alias, R. M. B. Chaves, and P. Mira, Bjorling problem for maximal surfaces in Lorentz-Minkowski space, Math. Proc. Camb. Phil. Soc., 134(2003), 289-326. crossref(new window)

3.
J. O. Baek, Q. M. Cheng, and Y. J. Suh, Complete space-like hypersurfaces in locally symmetric Lorentz space, J. Geometry and Physics, 49(2004), 231-247. crossref(new window)

4.
E. Calabi, Examples of Bernstein problems for some nonlinear equations, Proc. Symp. Pure Math., 15(1970), 223-230.

5.
S. Y. Chehg and S. T. Yau, Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces, Ann. Math., 104(1976), 407-419. crossref(new window)

6.
U. Dursun, On Minimal Hypersurfaces of Lorentzian Space Forms, Turk Matematik Dernegi XI. Ulusal Matematik Sempozyumu, Suleyman Demirel Universitesi, Isparta, Turkey, pp. 105-114, 1998.

7.
U. Dursun, On minimal and Chen immersions in space forms, J. Geom., 66(1999), 104-111. crossref(new window)

8.
M. Kimura, Minimal hypersurfaces foliated by geodesics of 4-dimensional space forms, Tokyo J. Math., 16(1993), 241-260. crossref(new window)

9.
O. Kobayashi, Maximal surfaces in 3-dimensional Minkowski space $L^{3}$, Tokyo J. Math., 6(1983), 297-309. crossref(new window)

10.
H. Li, On complete maximal space-like hypersurfaces in a Lorentz manifold, Soochow J. Math., 23(1)(1997), 79-89.

11.
J. J. Lopez, R. Lopez, and R. Souam, Maximal surfaces of Riemann type in Lorentz-Minkowski space $L^{3}$, Michigan Math. J., 47(3)(2000), 469-497. crossref(new window)

12.
J. E. Marsden and F. J. Tipler,Maximal hypersurfaces and foliations of constant mean curvature in relativity, Phys. Rep., 66(1980), 109-139. crossref(new window)

13.
P. Mira and J. A. PastorR, Helicoidal maximal surfaces Lorentz-Minkowski space, Monatsh. Math., 140(2003), 315-334. crossref(new window)

14.
S. Montiel, An integral inequality for compact space-like hypersurfaces in de Sitter space and applications to the case of constant mean curvature, Indiana Univ. Math. J., 37(4)(1988), 909-917. crossref(new window)

15.
H. Nishikawa, On maximal space-like hypersurfaces in a Lorentzian manifold, Nagoya Math. J., 95(1984), 117-124.

16.
B. O'Neill, Semi-Riemannian Geometry, Academic Press, New York, 1983.

17.
S. H. Park, Sphere-foliated minimal and constant mean curvature hypersurfaces in space forms and Lorentz-Minkowski space, Rocky Mountain J. Math., 32(2002), 1019-1044. crossref(new window)

18.
Y. J. Suh, Y. S. Choi, and H.Y. Yang, On space-like hypersurfaces with constant mean curvature in a Lorentz manifold, Houston J. Math., 28(1)(2002), 47-70.