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HOME > Table of Contents and Abstracts > Vol. 60, No. 4
Tohoku Mathematical Journal
2008
December
SECOND SERIES VOL. 60, NO. 4
Tohoku Math. J.
60 (2008), 499526

Title
CLASSIFICATION OF MÖBIUS ISOPARAMETRIC HYPERSURFACES IN THE UNIT SIXSPHERE
Dedicated to Professors Udo Simon and Seiki Nishikawa on the
occasion of their seventieth and sixtieth birthday
Author
Zejun Hu and Shujie Zhai
(Received October 11, 2007, revised April 28, 2008) 
Abstract.
An immersed umbilicfree hypersurface in the unit sphere is equipped with three Möbius invariants, namely, the Möbius metric, the Möbius second fundamental form and the Möbius form. The fundamental theorem of Möbius submanifolds geometry states that a hypersurface of dimension not less than three is uniquely determined by the Möbius metric and the Möbius second fundamental form. A Möbius isoparametric hypersurface is defined by two conditions that it has vanishing Möbius form and has constant Möbius principal curvatures. It is wellknown that all Euclidean isoparametric hypersurfaces are Möbius isoparametrics, whereas the latter are Dupin hypersurfaces. In this paper, combining with previous results, a complete classification for all Möbius isoparametric hypersurfaces in the unit sixsphere is established.
2000 Mathematics Subject Classification.
Primary 53A30; Secondary 53B25.
Key words and phrases.
Möbius isoparametric hypersurface, Möbius equivalence, Möbius second fundamental form, Möbius metric, Möbius form.


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