Möbius homogeneous hypersurfaces with three distinct principal curvatures in S ⁿ⁺¹

Abstract

Let x: M ⁿ → S ⁿ⁺¹ be an immersed hypersurface in the (n + 1)-dimensional sphere S ⁿ⁺¹. If, for any points p, q ∈ M ⁿ, there exists a Möbius transformation ϕ: S ⁿ⁺¹ → S ⁿ⁺¹ such that ϕ ○ x(M ⁿ) = x(M ⁿ) and ϕ ○ x(p) = x(q), then the hypersurface is called a Möbius homogeneous hypersurface. In this paper, the Möbius homogeneous hypersurfaces with three distinct principal curvatures are classified completely up to a Möbius transformation.

Keywords

Möbius transformation group / Conformal transformation group / Möbius homogeneous hypersurfaces / Möbius isoparametric hypersurfaces

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