Spacelike Dupin hypersurfaces in Lorentzian space forms
In this paper, a \textit{Dupin hypersurface} in the Lorentz space form \(M_1^{n+1} (c)\) is defined as follows: Consider a space-like hypersurface \(x:M^n \to M_1^{n+1} (c)\) and define a \textit{curvature surface} of \(M^n\) as a smooth connected submanifold \(S\) such that for each point \(p\in S\), the tangent space \(T_p(S)\) is equal to a principal space of the shape operator \(\mathcal{A}\) of \(M^n\) at \(p\). The hypersurface \(M^n\) is then called a Dupin hypersurface if along each curvature surface the associated principal curvature is constant. In the paper under review, the authors study space-like Dupin hypersurfaces from the point of view of conformal geometry. They give a local classification of such surfaces with constant Möbius curvatures, after showing that the Möbius curvatures are invariant under conformal transformations of \(M_1^{n+1} (c)\).
scientific article; zbMATH DE number 6902432