NEW PARAMETRIC REPRESENTATION OF A SURFACE \mathfrak{B}-PENCIL WITH A COMMON LINE OF CURVATURE

Author:

Vedat~As\.{i}l,~Talat~K\"{o}rpinar,~Sel\c{c}uk~Ba\c{s}

2010 Mathematics Subject Classification:

53A35.

Keywords:

Bishop frame, line of curvature, surface pencil.

Abstract:

In this paper, we study line of curvature on a surface in the Euclidean 3-space. By utilizing the Bishop frame, the surface pencil can be expressed as a linear combination of the components of the local frame in Euclidean 3-space. With this parametric representation, we derive the necessary and sufficient condition for the given curve to be the line of curvature on the surface.

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Vol. 9 (17), 2014