Complete hypersurfaces with constant scalar curvature in a sphere

Ximin Liu; Hongxia Li

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 3, page 567-575
  • ISSN: 0010-2628

Abstract

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In this paper, by using Cheng-Yau’s self-adjoint operator □ , we study the complete hypersurfaces in a sphere with constant scalar curvature.

How to cite

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Liu, Ximin, and Li, Hongxia. "Complete hypersurfaces with constant scalar curvature in a sphere." Commentationes Mathematicae Universitatis Carolinae 46.3 (2005): 567-575. <http://eudml.org/doc/249544>.

@article{Liu2005,
abstract = {In this paper, by using Cheng-Yau’s self-adjoint operator $\square $, we study the complete hypersurfaces in a sphere with constant scalar curvature.},
author = {Liu, Ximin, Li, Hongxia},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {hypersurface; sphere; scalar curvature; scalar curvature},
language = {eng},
number = {3},
pages = {567-575},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Complete hypersurfaces with constant scalar curvature in a sphere},
url = {http://eudml.org/doc/249544},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Liu, Ximin
AU - Li, Hongxia
TI - Complete hypersurfaces with constant scalar curvature in a sphere
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 3
SP - 567
EP - 575
AB - In this paper, by using Cheng-Yau’s self-adjoint operator $\square $, we study the complete hypersurfaces in a sphere with constant scalar curvature.
LA - eng
KW - hypersurface; sphere; scalar curvature; scalar curvature
UR - http://eudml.org/doc/249544
ER -

References

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  1. Alencar H., do Carmo M.P., Hypersurfaces with constant mean curvature in spheres, Proc. Amer. Math. Soc. 120 (1994), 1223-1229. (1994) Zbl0802.53017MR1172943
  2. Cheng S.Y., Yau S.T., Hypersurfaces with constant scalar curvature, Math. Ann. 225 (1977), 195-204. (1977) Zbl0349.53041MR0431043
  3. Hou Z.H., Hypersurfaces in sphere with constant mean curvature, Proc. Amer. Math. Soc. 125 (1997), 1193-1196. (1997) MR1363169
  4. Lawson H.B., Jr., Local rigidity theorems for minimal hypersurfaces, Ann. of Math. (2) 89 (1969), 187-197. (1969) Zbl0174.24901MR0238229
  5. Li H., Hypersurfaces with constant scalar curvature in space forms, Math. Ann. 305 (1996), 665-672. (1996) Zbl0864.53040MR1399710
  6. Nomizu K., Smyth B., A formula for Simon's type and hypersurfaces, J. Differential Geom. 3 (1969), 367-377. (1969) MR0266109
  7. Okumuru M., Hypersurfaces and a pinching problem on the second fundamental tensor, Amer. J. Math. 96 (1974), 207-213. (1974) MR0353216
  8. Omori H., Isometric immersions of Riemannian manifolds, J. Math. Soc. Japan 19 (1967), 205-214. (1967) Zbl0154.21501MR0215259
  9. Simons J., Minimal varieties in Riemannian manifolds, Ann. of Math. (2) 88 (1968), 62-105. (1968) Zbl0181.49702MR0233295
  10. Yau S.T., Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201-228. (1975) Zbl0291.31002MR0431040

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