Título: Hypersurfaces of S³xR and H³xR with constant principal curvatures

Palestrante: João Paulo dos Santos - Universidade de Brasília

Abstract.;

We classify the hypersurfaces of Q³_ε × R with three distinct constant principal curvatures, where ε ∈ {1, −1} and Q³ _ε denotes the unit sphere S ³ if ε = 1, whereas it denotes the hyperbolic space H³ if ε = −1. We show that they are cylinders over isopara- metric surfaces in Q³ _ε, filling an intriguing gap in the existing literature. We also prove that the hypersurfaces with constant principal curvatures of Q³ _ε × R are isoparametric. Furthermore, we provide the complete classification of the extrinsically homogeneous hy- persurfaces in Q³ _ε × R. This is a joint work with J. B. M. dos Santos, F. Manfio and J.Van der Veken.