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

Yaning Wang; Ximin Liu

Archivum Mathematicum (2012)

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

Abstract

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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.

How to cite

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Wang, 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

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  1. Chen, S. Y., Yau, S. T., 10.1007/BF01425237, Math. Ann. 225 (1977), 195–204. (1977) MR0431043DOI10.1007/BF01425237
  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. (1999) MR1744497
  3. 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
  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. (2010) MR2654420
  5. 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
  6. Liu, X. M., 10.1007/s002290100187, Manuscripta Math. 105 (2001), 367–377. (2001) MR1856617DOI10.1007/s002290100187
  7. Okumura, M., Hypersurfaces and a piching problem on the second fundamental thesor, J. Math. Soc. Japan 19 (1967), 205–214. (1967) 
  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. (2002) MR1876939
  9. Xu, S. L., Chen, D. M., 10.1007/BF02835231, Anal. Theory Appl. 20 (2004), 383–390. (2004) Zbl1080.53055MR2120013DOI10.1007/BF02835231
  10. Yau, S. T., 10.1002/cpa.3160280203, Comm. Pure Appl. Math. 28 (1975), 201–228. (1975) MR0431040DOI10.1002/cpa.3160280203
  11. 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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