Let [Formula: see text] be a parameter and an asymptotic curve on a surface [Formula: see text] We obtain conditions for offsets [Formula: see text] of [Formula: see text] such that the image [Formula: see text] of the curve [Formula: see text] is a common asymptotic on each offset. We illustrate the method with an example.
In the present paper, we handle the problem of finding a hypersurface family from a given asymptotic curve in R 4. Using the Frenet frame of the given asymptotic curve, we express the hypersurface as a linear combination of this frame and analyze the necessary and sufficient conditions for that curve to be asymptotic. We illustrate this method by presenting some examples.
In this paper, we analyze the problem of constructing a surface pencil from a
given spacelike (timelike) line of curvature. By using the Frenet frame of the
given curve in Minkowski 3-space, we express the surface pencil as a linear
combination of this frame and derive the necessary and sufficient conditions
for the coefficients to satisfy the line of curvature requirement. To
illustrate the method some examples showing members of the surface pencil with
their line of curvature are given.Comment: 23 pages, 6 figure
In the present paper, we construct surfaces possessing an adjoint curve of a given space curve as an asymptotic curve, geodesic or line of curvature. We obtain conditions for ruled surfaces and developable ones. Finally, we present illustrative examples to show the validity of the present method.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.