About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Liu, Ximin ; Li, Hongxia
Complete hypersurfaces with constant scalar curvature in a sphere. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 46 (2005), issue 3, pp. 567-575
MSC: 53A10, 53C21, 53C40, 53C42 | MR 2174533 | Zbl 1121.53006
Keywords:
hypersurface; sphere; scalar curvature
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.
References:
[1] Alencar H., do Carmo M.P.: Hypersurfaces with constant mean curvature in spheres. Proc. Amer. Math. Soc. 120 (1994), 1223-1229. MR 1172943 | Zbl 0802.53017
[2] Cheng S.Y., Yau S.T.: Hypersurfaces with constant scalar curvature. Math. Ann. 225 (1977), 195-204. MR 0431043 | Zbl 0349.53041
[3] Hou Z.H.: Hypersurfaces in sphere with constant mean curvature. Proc. Amer. Math. Soc. 125 (1997), 1193-1196. MR 1363169
[4] Lawson H.B., Jr.: Local rigidity theorems for minimal hypersurfaces. Ann. of Math. (2) 89 (1969), 187-197. MR 0238229 | Zbl 0174.24901
[5] Li H.: Hypersurfaces with constant scalar curvature in space forms. Math. Ann. 305 (1996), 665-672. MR 1399710 | Zbl 0864.53040
[6] Nomizu K., Smyth B.: A formula for Simon's type and hypersurfaces. J. Differential Geom. 3 (1969), 367-377. MR 0266109
[7] Okumuru M.: Hypersurfaces and a pinching problem on the second fundamental tensor. Amer. J. Math. 96 (1974), 207-213. MR 0353216
[8] Omori H.: Isometric immersions of Riemannian manifolds. J. Math. Soc. Japan 19 (1967), 205-214. MR 0215259 | Zbl 0154.21501
[9] Simons J.: Minimal varieties in Riemannian manifolds. Ann. of Math. (2) 88 (1968), 62-105. MR 0233295 | Zbl 0181.49702
[10] Yau S.T.: Harmonic functions on complete Riemannian manifolds. Comm. Pure Appl. Math. 28 (1975), 201-228. MR 0431040 | Zbl 0291.31002
Partner of
EuDML logo