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- W4290978859 abstract "We study surfaces with one constant principal curvature in Riemannian and Lorentzian three-dimensional space forms. Away from umbilic points they are characterized as one-parameter foliations by curves of constant curvature, each of these curves being centered at a point of a regular curve and contained in its normal plane. In some cases, a kind of trichotomy phenomenon is observed: the curves of the foliations may be circles, hyperbolas or horocycles, depending of whether the constant principal curvature is respectively larger, smaller of equal to one (not necessarily in this order). We describe explicitly some examples showing that there do exist complete surfaces with one constant principal curvature enjoying both umbilic and non-umbilic points." @default.
- W4290978859 created "2022-08-13" @default.
- W4290978859 creator A5004070879 @default.
- W4290978859 date "2013-07-25" @default.
- W4290978859 modified "2023-10-18" @default.
- W4290978859 title "Surfaces with one constant principal curvature in three-dimensional space forms" @default.
- W4290978859 doi "https://doi.org/10.48550/arxiv.1307.6735" @default.
- W4290978859 hasPublicationYear "2013" @default.
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