Arkiv för Matematik

  • Ark. Mat.
  • Volume 51, Number 2 (2013), 315-328.

Möbius homogeneous hypersurfaces with two distinct principal curvatures in Sn+1

Tongzhu Li, Xiang Ma, and Changping Wang

Full-text: Open access

Abstract

The purpose of this paper is to classify the Möbius homogeneous hypersurfaces with two distinct principal curvatures in Sn+1 under the Möbius transformation group. Additionally, we give a classification of the Möbius homogeneous hypersurfaces in S4.

Article information

Source
Ark. Mat., Volume 51, Number 2 (2013), 315-328.

Dates
Received: 24 April 2011
First available in Project Euclid: 1 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907213

Digital Object Identifier
doi:10.1007/s11512-011-0161-5

Mathematical Reviews number (MathSciNet)
MR3090199

Rights
2011 © Institut Mittag-Leffler

Citation

Li, Tongzhu; Ma, Xiang; Wang, Changping. Möbius homogeneous hypersurfaces with two distinct principal curvatures in S n +1. Ark. Mat. 51 (2013), no. 2, 315--328. doi:10.1007/s11512-011-0161-5. https://projecteuclid.org/euclid.afm/1485907213


Export citation

References

  • Akivis, M. V. and Goldberg, V. V., A conformal differential invariant and the conformal rigidity of hypersurfaces, Proc. Amer. Math. Soc. 125 (1997), 2415–2424.
  • Cartan, É., Sur des familles remarquables d’hypersurfaces isoparamétriques dans les espaces sphériques, Math. Z. 45 (1939), 335–367.
  • Guo, Z., Li, H. and Wang, C., The Möbius characterizations of Willmore tori and Veronese submanifolds in the unit sphere, Pacific J. Math. 241 (2009), 227–242.
  • Hu, Z. J. and Li, D., Möbius isoparametric hypersurfaces with three distinct principal curvatures, Pacific J. Math. 232 (2007), 289–311.
  • Li, H., Liu, H., Wang, C. and Zhao, G., Moebius isoparametric hypersurfaces in Sn+1 with two distinct principal curvatures, Acta Math. Sin. (Engl. Ser.) 18 (2002), 437–446.
  • Li, X. and Zhang, F., On the Blaschke isoparametric hypersurfaces in the unit sphere, Acta Math. Sin. (Engl. Ser.) 25 (2009), 657–678.
  • Liu, H., Wang, C. and Zhao, G., Möbius isotropic submanifolds in Sn, Tohoku Math. J. 53 (2001), 553–569.
  • O’Neil, B., Semi-Riemannian Geometry, Academic Press, New York, 1983.
  • Sulanke, R., Möbius geometry V: Homogeneous surfaces in the Möbius space S3, in Topics in Differential Geometry (Debrecen, 1984 ), vol. 2, pp. 1141–1154, Colloq. Math. Soc. János Bolyai 46, North-Holland, Amsterdam, 1988.
  • Wang, C., Möbius geometry for hypersurfaces in S4, Nagoya Math. J. 139 (1995), 1–20.
  • Wang, C., Möbius geometry of submanifolds in Sn, Manuscripta Math. 96 (1998), 517–534.