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- W3137865744 abstract "In this paper, we first prove that the only surface (other then a sphere) on which the two families of Darboux lines form a Tschebycheff net and the third family of Darboux lines is transversal to one of the two families of Darboux lines is a cylinder of revolution. We next show that the surface (other than a sphere or a developable surface) on which the Darboux lines correspond to those on its parallel surface is a surface of constant mean curvature. Moreover, if the two families of Darboux lines on a surface of constant mean curvature form a Tschebyscheff net, then a surface becomes a cylinder of revolution or a plane. Furthermore, we prove that surfaces (other than a sphere or a plane) whose Darboux lines are preserved under inversion are Dupin's cyclides or, in particular, a pipe surface of revolution. Finally, we show that Molure surface on which the two families of Darboux lines which are different from the lines of curvature form two semi-Tschebyscheff nets together with a family of lines of curvature are either a surface of revolution or a pipe surface." @default.
- W3137865744 created "2021-03-29" @default.
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- W3137865744 date "2020-05-31" @default.
- W3137865744 modified "2023-09-26" @default.
- W3137865744 title "ON DARBOUX LINES" @default.
- W3137865744 hasPublicationYear "2020" @default.
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