Curvature homogeneous hypersurfaces in space forms
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We provide a classification of curvature homogeneous hypersurfaces in space forms by classifying the ones in and . In higher dimensions, besides the isoparametric and the constant curvature ones, there is a single one in . Besides the obvious examples, we show that there exists an isolated hypersurface with a circle of symmetries and a one parameter family admitting no continuous symmetries. Outside the set of minimal points, which only exists in the case of , every example is, locally and up to covers, of this form.
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Bryant, Robert, Wolfgang Ziller and Luis Florit (n.d.). Curvature homogeneous hypersurfaces in space forms. Advances in Mathematics. 10.1016/j.aim.2025.110338 Retrieved from https://hdl.handle.net/10161/32393.
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