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A nonisoparametric hypersurface with constant principal curvatures


Author: Alberto Rodríguez-Vázquez
Journal: Proc. Amer. Math. Soc. 147 (2019), 5417-5420
MSC (2010): Primary 53C40; Secondary 53B25, 53C12
DOI: https://doi.org/10.1090/proc/14654
Published electronically: June 10, 2019
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Abstract: In this note we construct an explicit example of a (compact) conformally flat Riemannian manifold which admits a totally geodesic foliation of codimension one with no isoparametric leaves. This answers negatively the question: Is every hypersurface with constant principal curvatures isoparametric?


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Additional Information

Alberto Rodríguez-Vázquez
Affiliation: Department of Mathematics, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
Email: a.rodriguez@usc.es

DOI: https://doi.org/10.1090/proc/14654
Keywords: Isoparametric hypersurface, constant principal curvatures
Received by editor(s): March 19, 2019
Published electronically: June 10, 2019
Additional Notes: The author was supported by the project MTM2016-75897-P (AEI/FEDER, Spain) and an FPU fellowship from Ministerio de Ciencia, Innovación y Universidades.
Communicated by: Jiaping Wang
Article copyright: © Copyright 2019 American Mathematical Society