Abstract
The conformal geometry of regular hypersurfaces in the conformal space is studied. We classify all the conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in the conformal space up to conformal equivalence.
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Hu Z J, Li H Z. Classification of hypersurfaces with parallel Möbius second fundamental form in Sn+1. SciChina Ser A, 2004, 47: 417–430
Li H Z, Liu H L, Wang C P, et al. Möbius isoparametric hypersurfaces in Sn+1 with two distinct principal curvatures. Acta Math Sinica Engl Ser, 2002, 18: 437–446
Li Z Q, Xie Z H. Space-like isoparametric hypersurfaces in Lorentzian space forms. Front Math China, 2006, 1: 130–137
Magid M A. Lorentzian isoparametric hypersurface. Pacific J Math, 1985, 118: 437–446
Nie C X. Conformal geometry of hypersurfaces and surfaces in Lorentzian space forms (in Chinese). Dissertation for the Doctoral Degree. Beijing: Peking University, 2006, 17–27, 41–52
Nie C X, Ma X, Wang C P. Conformal CMC-surfaces in Lorentzian space forms. Chin Ann Math Ser B, 2007, 28: 299–310
Nie C X, Wu C X. Regular submanifolds in conformal spaces (in Chinese). Chin Ann Math Ser A, 2008, 29: 315–324
Nie C X, Wu C X. Space-like hyperspaces with parallel conformal second fundamental forms in the conformal space (in Chinese). Acta Math Sinica Chin Ser, 2008, 51: 685–692
Nomizu K. On isoparametric hypersurfaces in the Lorentzian space forms. Japan J Math, 1981, 7: 217–216
Xiao L. Lorentzian isoparametric hypersurfaces in H n+11 . Pacific J Math, 1999, 189: 377–397
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Nie, C., Li, T., He, Y. et al. Conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in conformal space. Sci. China Math. 53, 953–965 (2010). https://doi.org/10.1007/s11425-009-0206-4
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DOI: https://doi.org/10.1007/s11425-009-0206-4