In this paper, we analyzed
surfaces family possessing a Mannheim partner of a given curve as a asymptotic.
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
asymptotic and isoparametric requirements. The extension to ruled surfaces is
also outlined. Finally, examples are given to show the family of surfaces with
common Mannheim asymptotic curve.
How to cite this paper
Surfaces family with a common Mannheim asymptotic curve
How to cite this paper: ATALAY, G.Ş. (2018) Surfaces family with a common Mannheim asymptotic curve. Journal of Applied Mathematics and Computation, 2(4), 143-154.