Hypersurfaces with planar lines of curvature in Euclidean Space
DOI:
https://doi.org/10.17268/sel.mat.2017.02.02Keywords:
Sphere congruence, Laplace invariants, lines of curvature, isothermic surfacesAbstract
In this work, we present explicit parameterizations of hypersurfaces parameterized by lines of curvature with prescribed Gauss map and we characterize the hypersurfaces with planar curvature lines. As an application
we obtain a classification of isothermic surfaces with respect to the third fundamental form with two planar curvature lines. Also, we present a class of surfaces with one family of planar curvature lines and generalize these results to present classes of hypersurfaces with families of planar curvature lines.
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