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| Möbius Homogeneous Hypersurfaces with Three Distinct Principal Curvatures in Sn+1 |
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Citation： |
Tongzhu LI.Möbius Homogeneous Hypersurfaces with Three Distinct Principal Curvatures in Sn+1[J].Chinese Annals of Mathematics B,2017,38(5):1131~1144 |
| Page view： 2850
Net amount： 1307 |
Authors： |
Tongzhu LI; |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11571037, 11471021). |
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| Abstract： |
Let $x:M^n\to \mathbb{S}^{n+1}$ be an immersed hypersurface in the
$(n+1)$-dimensional sphere $\mathbb{S}^{n+1}$. If, for any points
$p,q\in M^n$, there exists a M\"{o}bius transformation
$\phi:\mathbb{S}^{n+1}\to\mathbb{S}^{n+1}$ such that $\phi\circ
x(M^n)=x(M^n)$ and $\phi\circ x(p)=x(q)$, then the hypersurface is
called a M\"{o}bius homogeneous hypersurface. In this paper, the
M\"{o}bius homogeneous hypersurfaces with three distinct principal
curvatures are classified completely up to a M\"{o}bius
transformation. |
Keywords： |
M\"{o}bius transformation group, Conformal transformation group,
M\"{o}bius homogeneous hypersurfaces, M\"{o}bius isoparametric
hypersurfaces |
Classification： |
53A30, 53C40 |
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