Surface Family With a Common Mannheim B-Geodesic Curve

Abstract

In this paper, we construct a surface family possessing a Mannheim B pair of a given curve as a geodesic curve. Using the Bishop frame of the given Mannheim B curves, we present the surface as a linear combination of this frame and analyse the necessary and sufficient condition for a given curve such that its Mannheim B pairs is both isoparametric and geodesic on a parametric surface. Also we analyze the conditions when the resulting surface is a ruled surface. In addition, developability along the common Mannheim B -geodesic of the members of surface family are discussed. Finally, we present some interesting examples to show the validity of this study. © 2021 Balkan Society of Geometers, Geometry Balkan Press. All Rights Reserved.