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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.