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arXiv · 2404.02302

Curvature homogeneous hypersurfaces in space forms

Robert Bryant·Luis Florit·Wolfgang Ziller
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Abstract

We classify curvature homogeneous hypersurfaces in S^4 and H^4. In higher dimesnsion one only has the FKM examples and an isolate one by Tsukada of a hypersurface in H^5. Besides some simple examples, we show that there exists an isolated hypersurface with a circle of symmetries and and a one parameter family admitting no continuous symmetries. Outside the set of minimal points, which only exists in the case of S^4, every example is locally and up to covers of this form.

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Robert Bryant, Luis Florit, Wolfgang Ziller. 2024-04-02. Curvature homogeneous hypersurfaces in space forms. https://arxiv.org/abs/2404.02302

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