Isoparametric surfaces in E(κ, τ)-spaces

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URI: http://hdl.handle.net/10347/35022
DOI: 10.2422/2036-2145.201805_006

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2021

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Scuola Normale Superiore
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We provide an explicit classification of the following four families of surfaces in any homogeneous 3-manifold with 4-dimensional isometry group: isoparametric surfaces, surfaces with constant principal curvatures, homogeneous surfaces, and surfaces with constant mean curvature and vanishing Abresch-Rosenberg differential.

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Homogeneous 3-manifolds| Constant principal curvatures| Homogeneous surfaces| Isoparametric surfaces

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Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 22 (2021), 269-285

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The first author acknowledges support by the projects MTM2016-75897-P, PID2019-105138GB-C21(AEI/FEDER, Spain), ED431C2019/10, ED431F2020/04 (Xunta de Galicia, Spain), and the EU’s Horizon2020 programme under the Marie Sklodowska-Curie grant agreement No. 745722. The second author is supported by the MINECO-FEDER projects MTM2017-89677-P and PID2019-111531GA-I00/AEI/10.13039/501100011033. Both authors have been supported by the Ramón y Cajal programme of the Spanish Ministry of Science.

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