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	Classification of Mobius isoparametric hypersurfaces in S-5
	Hu, Zejun ; Li, Haizhong ; Wang, Changping
	2010-05-06 ; 2010-05-06
关键词	Mobius isoparametric hypersurface Mobius metric Mobius equivalence DUPIN HYPERSURFACES S-N PRINCIPAL CURVATURES SUBMANIFOLDS SURFACES FORM R5 Mathematics
中文摘要	Let M-n be an immersed umbilic-free hypersurface in the (n + 1)-dimensional unit sphere Sn+1, then M-n is associated with a so-called Mobius metric g, a Mobius second fundamental form B and a Mobius form Phi which are invariants of M-n under the Mobius transformation group of Sn+1. A classical theorem of Mobius geometry states that M-n(n >= 3) is in fact characterized by g and B up to Mobius equivalence. A Mobius isoparametric hypersurface is defined by satisfying two conditions: (1) Phi 0; (2) All the eigenvalues of B with respect to g are constants. Note that Euclidean isoparametric hypersurfaces are automatically Mobius isoparametrics, whereas the latter are Dupin hypersurfaces. In this paper, we determine all Mobius isoparametric hypersurfaces in S-5 by proving the following classification theorem: If x : M -> S-5 is a Mobius isoparametric hypersurface, then x is Mobius equivalent to either (i) a hypersurface having parallel Mobius second fundamental form in S-5; or (ii) the pre-image of the stereographic projection of the cone in R-5 over the Cartan isoparametric hypersurface in S-4 with three distinct principal curvatures; or (iii) the Euclidean isoparametric hypersurface with four principal curvatures in S-5. The classification of hypersurfaces in Sn+1 (n >= 2) with parallel Mobius second fundamental form has been accomplished in our previous paper [7]. The present result is a counterpart of the classification for Dupin hypersurfaces in E 5 up to Lie equivalence obtained by R. Niebergall, T. Cecil and G. R. Jensen.
语种	英语 ; 英语
出版者	SPRINGER WIEN ; WIEN ; SACHSENPLATZ 4-6, PO BOX 89, A-1201 WIEN, AUSTRIA
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/13704]
专题	清华大学
推荐引用方式 GB/T 7714	Hu, Zejun,Li, Haizhong,Wang, Changping. Classification of Mobius isoparametric hypersurfaces in S-5[J],2010, 2010.
APA	Hu, Zejun,Li, Haizhong,&Wang, Changping.(2010).Classification of Mobius isoparametric hypersurfaces in S-5..
MLA	Hu, Zejun,et al."Classification of Mobius isoparametric hypersurfaces in S-5".(2010).

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