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- W2018461949 abstract "A surface F2 in E4 is called function-degenerate if parameters α, β, a, and b of the ellipse of normal curvature (α and β are the coordinates of its center in the normal plane and a and b are the values of the semiaxes) are some functions of a function t(P) of point P of the surface. This class of surfaces is a generalization of the class of surfaces that admit motion with respect to themselves along some family of lines. The following theorem is proved: There does not exist a regular, class C6, isometric immersion of the Lobachevsky plane L2 into E4, with zero Gaussian torsion, in the form of a function-degenerate surface. This theorem includes the Hilbert theorem on surfaces of negative curvature in E3." @default.
- W2018461949 created "2016-06-24" @default.
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- W2018461949 date "1991-02-01" @default.
- W2018461949 modified "2023-10-16" @default.
- W2018461949 title "On function-degenerate immersions of a Lobachevsky plane into E4" @default.
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- W2018461949 doi "https://doi.org/10.1007/bf01109644" @default.
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