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Given a Riemannian manifold M, and an open interval I ⊂ R, we characterize nontrivial totally umbilical hypersurfaces of the product M×I — as well as of warped products I… Click to show full abstract
Given a Riemannian manifold M, and an open interval I ⊂ R, we characterize nontrivial totally umbilical hypersurfaces of the product M×I — as well as of warped products I ×ω M — as those which are local graphs built on isoparametric families of totally umbilical hypersurfaces of M. By means of this characterization, we fully extend to Sn × R and Hn × R the results by Souam and Toubiana on the classification of totally umbilical hypersurfaces of S2 × R and H2 × R. It is also shown that an analogous classification holds for arbitrary warped products I ×ω Sn and I ×ω Hn.
Journal Title: manuscripta mathematica
Year Published: 2021
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