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 A note on compact M\"{o}bius homogeneous submanifolds in $\mathbb{S}^{n+1}$ Bull. Korean Math. Soc. 2019 Vol. 56, No. 3, 681-689 https://doi.org/10.4134/BKMS.b180491Published online May 31, 2019 Xiu Ji, TongZhu Li Beijing Institute of Technology; Beijing Institute of Technology Abstract : 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 Full-Text :