# Compact space-like hypersurfaces with constant scalar curvature in locally symmetric Lorentz spaces

Archivum Mathematicum (2012)

- Volume: 048, Issue: 3, page 163-172
- ISSN: 0044-8753

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topWang, Yaning, and Liu, Ximin. "Compact space-like hypersurfaces with constant scalar curvature in locally symmetric Lorentz spaces." Archivum Mathematicum 048.3 (2012): 163-172. <http://eudml.org/doc/247009>.

@article{Wang2012,

abstract = {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.},

author = {Wang, Yaning, Liu, Ximin},

journal = {Archivum Mathematicum},

keywords = {space-like hypersurface; constant scalar curvature; second fundamental form; locally symmetric Lorentz space; space-like hypersurface; constant scalar curvature; second fundamental form; locally symmetric Lorentz space},

language = {eng},

number = {3},

pages = {163-172},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Compact space-like hypersurfaces with constant scalar curvature in locally symmetric Lorentz spaces},

url = {http://eudml.org/doc/247009},

volume = {048},

year = {2012},

}

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

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 048

IS - 3

SP - 163

EP - 172

AB - 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.

LA - eng

KW - space-like hypersurface; constant scalar curvature; second fundamental form; locally symmetric Lorentz space; space-like hypersurface; constant scalar curvature; second fundamental form; locally symmetric Lorentz space

UR - http://eudml.org/doc/247009

ER -

## References

top- Chen, S. Y., Yau, S. T., 10.1007/BF01425237, Math. Ann. 225 (1977), 195–204. (1977) MR0431043DOI10.1007/BF01425237
- Choi, S. M., Kwon, J. H., Suh, Y. J., Complete spacelike hypersurfaces in a Lorentz manifold, Math. J. Toyama Univ. 22 (1999), 53–76. (1999) MR1744497
- Jin, O. B., Cheng, Q. M., Young, J. S., 10.1016/S0393-0440(03)00090-1, J. Geom. Phys. 49 (2004), 231–247. (2004) MR2077302DOI10.1016/S0393-0440(03)00090-1
- 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. (2010) MR2654420
- Liu, X., Space-like hypersurfaces of constant scalar in the de Sitter space, Atti Sem. Mat. Fis. Univ. Modena 48 (2000), 99–106. (2000) MR1767413
- Liu, X. M., 10.1007/s002290100187, Manuscripta Math. 105 (2001), 367–377. (2001) MR1856617DOI10.1007/s002290100187
- Okumura, M., Hypersurfaces and a piching problem on the second fundamental thesor, J. Math. Soc. Japan 19 (1967), 205–214. (1967)
- 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. (2002) MR1876939
- Xu, S. L., Chen, D. M., 10.1007/BF02835231, Anal. Theory Appl. 20 (2004), 383–390. (2004) Zbl1080.53055MR2120013DOI10.1007/BF02835231
- Yau, S. T., 10.1002/cpa.3160280203, Comm. Pure Appl. Math. 28 (1975), 201–228. (1975) MR0431040DOI10.1002/cpa.3160280203
- Zheng, Y. F., 10.1016/0926-2245(96)00006-X, Differential Geom. Appl. 6 (1996), 51–54. (1996) MR1384878DOI10.1016/0926-2245(96)00006-X

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