| Title:
|
Complete hypersurfaces with constant scalar curvature in a sphere (English) |
| Author:
|
Liu, Ximin |
| Author:
|
Li, Hongxia |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
567-575 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, by using Cheng-Yau's self-adjoint operator $\square$, we study the complete hypersurfaces in a sphere with constant scalar curvature. (English) |
| Keyword:
|
hypersurface |
| Keyword:
|
sphere |
| Keyword:
|
scalar curvature |
| MSC:
|
53A10 |
| MSC:
|
53C21 |
| MSC:
|
53C40 |
| MSC:
|
53C42 |
| idZBL:
|
Zbl 1121.53006 |
| idMR:
|
MR2174533 |
| . |
| Date available:
|
2009-05-05T16:53:24Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119549 |
| . |
| Reference:
|
[1] Alencar H., do Carmo M.P.: Hypersurfaces with constant mean curvature in spheres.Proc. Amer. Math. Soc. 120 (1994), 1223-1229. Zbl 0802.53017, MR 1172943 |
| Reference:
|
[2] Cheng S.Y., Yau S.T.: Hypersurfaces with constant scalar curvature.Math. Ann. 225 (1977), 195-204. Zbl 0349.53041, MR 0431043 |
| Reference:
|
[3] Hou Z.H.: Hypersurfaces in sphere with constant mean curvature.Proc. Amer. Math. Soc. 125 (1997), 1193-1196. MR 1363169 |
| Reference:
|
[4] Lawson H.B., Jr.: Local rigidity theorems for minimal hypersurfaces.Ann. of Math. (2) 89 (1969), 187-197. Zbl 0174.24901, MR 0238229 |
| Reference:
|
[5] Li H.: Hypersurfaces with constant scalar curvature in space forms.Math. Ann. 305 (1996), 665-672. Zbl 0864.53040, MR 1399710 |
| Reference:
|
[6] Nomizu K., Smyth B.: A formula for Simon's type and hypersurfaces.J. Differential Geom. 3 (1969), 367-377. MR 0266109 |
| Reference:
|
[7] Okumuru M.: Hypersurfaces and a pinching problem on the second fundamental tensor.Amer. J. Math. 96 (1974), 207-213. MR 0353216 |
| Reference:
|
[8] Omori H.: Isometric immersions of Riemannian manifolds.J. Math. Soc. Japan 19 (1967), 205-214. Zbl 0154.21501, MR 0215259 |
| Reference:
|
[9] Simons J.: Minimal varieties in Riemannian manifolds.Ann. of Math. (2) 88 (1968), 62-105. Zbl 0181.49702, MR 0233295 |
| Reference:
|
[10] Yau S.T.: Harmonic functions on complete Riemannian manifolds.Comm. Pure Appl. Math. 28 (1975), 201-228. Zbl 0291.31002, MR 0431040 |
| . |
