Geodesic
Compact space-like hypersurfaces with constant scalar curvature in locally symmetric Lorentz spaces
Archivum mathematicum, Tome 48 (2012) no. 3, pp. 163-172 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

A new class of $(n+1)$-dimensional Lorentz spaces of index $1$ is introduced which satisfies some geometric conditions and can be regarded as a generalization of Lorentz space form. Then, the compact space-like hypersurface with constant scalar curvature of this spaces is investigated and a gap theorem for the hypersurface is obtained.
A new class of $(n+1)$-dimensional Lorentz spaces of index $1$ is introduced which satisfies some geometric conditions and can be regarded as a generalization of Lorentz space form. Then, the compact space-like hypersurface with constant scalar curvature of this spaces is investigated and a gap theorem for the hypersurface is obtained.
DOI : 10.5817/AM2012-3-163
Classification : 53C15, 53C42
Keywords: space-like hypersurface; constant scalar curvature; second fundamental form; locally symmetric Lorentz space 
@article{10_5817_AM2012_3_163,
     author = {Wang, Yaning and Liu, Ximin},
     title = {Compact space-like hypersurfaces  with constant scalar curvature in locally symmetric {Lorentz} spaces},
     journal = {Archivum mathematicum},
     pages = {163--172},
     year = {2012},
     volume = {48},
     number = {3},
     doi = {10.5817/AM2012-3-163},
     mrnumber = {2995869},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2012-3-163/}
}
TY  - JOUR
AU  - Wang, Yaning
AU  - Liu, Ximin
TI  - Compact space-like hypersurfaces  with constant scalar curvature in locally symmetric Lorentz spaces
JO  - Archivum mathematicum
PY  - 2012
SP  - 163
EP  - 172
VL  - 48
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2012-3-163/
DO  - 10.5817/AM2012-3-163
LA  - en
ID  - 10_5817_AM2012_3_163
ER  - 
%0 Journal Article
%A Wang, Yaning
%A Liu, Ximin
%T Compact space-like hypersurfaces  with constant scalar curvature in locally symmetric Lorentz spaces
%J Archivum mathematicum
%D 2012
%P 163-172
%V 48
%N 3
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2012-3-163/
%R 10.5817/AM2012-3-163
%G en
%F 10_5817_AM2012_3_163
Wang, Yaning; Liu, Ximin. Compact space-like hypersurfaces  with constant scalar curvature in locally symmetric Lorentz spaces. Archivum mathematicum, Tome 48 (2012) no. 3, pp. 163-172. doi: 10.5817/AM2012-3-163

[1] Chen, S. Y., Yau, S. T.: Hypersurfaces with constant scalar curvature. Math. Ann. 225 (1977), 195–204. | DOI | MR

[2] Choi, S. M., Kwon, J. H., Suh, Y. J.: Complete spacelike hypersurfaces in a Lorentz manifold. Math. J. Toyama Univ. 22 (1999), 53–76. | MR

[3] Jin, O. B., Cheng, Q. M., Young, J. S.: Complete spacelike hypersurfaces in locally symmetric Lorentz space. J. Geom. Phys. 49 (2004), 231–247. | DOI | MR

[4] Liu, J. C., Wei, L.: A gep theorem for complete spacelike hypersurface with constant scalar curvature in locally symmetric Lorentz space. Turkish J. Math. 34 (2010), 105–114. | MR

[5] Liu, X.: Space-like hypersurfaces of constant scalar in the de Sitter space. Atti Sem. Mat. Fis. Univ. Modena 48 (2000), 99–106. | MR

[6] Liu, X. M.: Complete spacelike hypersurfaces with constant scalar curvature. Manuscripta Math. 105 (2001), 367–377. | DOI | MR

[7] Okumura, M.: Hypersurfaces and a piching problem on the second fundamental thesor. J. Math. Soc. Japan 19 (1967), 205–214.

[8] Suh, Y. J., Choi, Y. S., Yang, H. Y.: On spacelike hypersurfaces with constant mean curvature in Lorentz manifold. Houston J. Math. 28 (2002), 47–70. | MR

[9] Xu, S. L., Chen, D. M.: Complete space-like submanifolds in locally symmetric semi-definite spaces. Anal. Theory Appl. 20 (2004), 383–390. | DOI | MR | Zbl

[10] Yau, S. T.: Harmonic functions on complete Riemannian manifolds. Comm. Pure Appl. Math. 28 (1975), 201–228. | DOI | MR

[11] Zheng, Y. F.: Spacelike hypersurfaces with constant scalar curvature in the de Sitter space. Differential Geom. Appl. 6 (1996), 51–54. | DOI | MR

Cité par Sources :