In this paper, we analyzed
surfaces family possessing a Mannheim partner curve of a given curve as a
geodesic. Using the Frenet frame of the curve in Euclidean 3-space, we express
the family of surfaces as a linear combination of the components of this frame
and derive the necessary and sufficient conditions for coefficients to satisfy
both the geodesic and isoparametric requirements. The extension to ruled
surfaces is also outlined. Finally, examples are given to show the family of
surfaces with common Mannheim geodesic curve.
How to cite this paper
Surfaces family with a common Mannheim geodesic curve
How to cite this paper: ATALAY, G.Ş. (2018) Surfaces family with a common Mannheim geodesic curve. Journal of Applied Mathematics and Computation, 2(4), 155-165.