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The Surfaces which have on ortogonal net making constant angle lines of curvature

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2003
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Abstract (EN)

In this study, the surfaces having an orthogonal net on which are some lines of curvature that make a constant angle are written. And to have an orthogonal net on a surface needs to have a connection between geodesic curvature and Gauss curvature. If the surface is trivial, it shows it is a cylinder. To sum up, the surfaces, on which the bisectors of the lines of curvature make a isometric net are studied and as a result. (1) Only the three of the constant Gauss curvature surfaces have the some qualities. (2) The surfaces which haven't a constant Gauss curvature are divided into two groups and all the surfaces which belong to one of these groups are defined. A formula which is connected with the Gauss curvature of the surfaces of the other group is made up. A part from that quite a simple formula about the surfaces keeping the lines of curvature and having an isometry is also given.

Author

Yasemin Güllük

How to Cite

Yasemin Güllük (Master Thesis). The Surfaces which have on ortogonal net making constant angle lines of curvature, 2003, Yıldız Technical University.

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