Bull. Korean Math. Soc. 2019; 56(3): 681-689
Online first article October 29, 2018 Printed May 31, 2019
https://doi.org/10.4134/BKMS.b180491
Copyright © The Korean Mathematical Society.
Xiu Ji, TongZhu Li
Beijing Institute of Technology; Beijing Institute of Technology
The M\"{o}bius homogeneous submanifold in $\mathbb{S}^{n+1}$ is an orbit of a subgroup of the M\"{o}bius transformation group of $\mathbb{S}^{n+1}$. In this note, We prove that a compact M\"{o}bius homogeneous submanifold in $\mathbb{S}^{n+1}$ is the image of a M\"{o}bius transformation of the isometric homogeneous submanifold in $\mathbb{S}^{n+1}$.
Keywords: M\"{o}bius transformation group, isometric transformation group, M\"{o}bius homogeneous hypersurfaces, homogeneous hypersurfaces
MSC numbers: 53A30, 53C30
Supported by: Authors are partially supported by the grant No.11471021 and No. 11571037 of NSFC
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