Time-Like Conformal Homogeneous Hypersurfaces with Three Distinct Principal Curvatures

Abstract

A hypersurface x(M) in Lorentzian space R ₁ ⁴ is called conformal homogeneous, if for any two points p, q on M, there exists σ, a conformal transformation of R ₁ ⁴, such that σ(x(M)) = x(M), σ(x(p)) = x(q). In this paper, the authors give a complete classification for regular time-like conformal homogeneous hypersurfaces in R ₁ ⁴ with three distinct principal curvatures.

Keywords

Lorentzian metric / Conformal metric / Conformal space form / Conformal homogeneous / Time-like hypersurface

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