| Title:
|
The first eigenvalue of spacelike submanifolds in indefinite space form $R^{n+p}_p$ (English) |
| Author:
|
Han, Yingbo |
| Author:
|
Feng, Shuxiang |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
47 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
77-82 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we prove that the first eigenvalue of a complete spacelike submanifold in $R^{n+p}_p$ with the bounded Gauss map must be zero. (English) |
| Keyword:
|
spacelike submanifolds |
| Keyword:
|
the first eigenvalue |
| MSC:
|
53B30 |
| MSC:
|
53C42 |
| idZBL:
|
Zbl 1249.53076 |
| idMR:
|
MR2813533 |
| . |
| Date available:
|
2011-06-06T14:37:12Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141555 |
| . |
| Reference:
|
[1] Cheng, S. Y., Yau, S. T.: Differential equations on Riemannian manifolds and geometric applications.Comm. Pure Appl. Math. 28 (1975), 333–354. MR 0385749, 10.1002/cpa.3160280303 |
| Reference:
|
[2] Kobayashi, S., Nomizu, K.: Foundations of differential geometry.John Wiley & Sons, Inc., 1969. Zbl 0175.48504 |
| Reference:
|
[3] Wong, Y. C.: Euclidean n-space in pseudo-Euclidean spaces and differential geometry of Cartan domain.Bull. Amer. Math. Soc. (N.S.) 75 (1969), 409–414. MR 0251655, 10.1090/S0002-9904-1969-12198-1 |
| Reference:
|
[4] Wu, B. Y.: On the volume and Gauss map image of spacelike submanifolds in de Sitter space form.J. Geom. Phys. 53 (2005), 336–344. Zbl 1078.53063, MR 2108534, 10.1016/j.geomphys.2004.07.003 |
| Reference:
|
[5] Wu, B. Y.: On the first eigenvalue of spacelike hypersurfaces in Lorentzian space.Arch. Math. (Brno) 42 (2006), 233–238. Zbl 1164.53373, MR 2260381 |
| Reference:
|
[6] Xin, Y. L.: A rigidity theorem for spacelike graph of higher codimension.Manuscripta Math. 103 (2000), 191–202. MR 1796315, 10.1007/s002290070020 |
| . |
