[PDF][PDF] Surfaces family with common Smarandache geodesic curve
In this paper, we analyzed the problem of finding a surfaces family through a given some
special Smarandache curves in Euclidean 3-space. Using the Frenet frame of the curve in …
special Smarandache curves in Euclidean 3-space. Using the Frenet frame of the curve in …
HYPERSURFACE FAMILIES WITH SMARANDACHE CURVES IN GALILEAN 4-SPACE.
In this paper, we study the hypersurface families with Smarandache curves in 4-dimensional
Galilean space G4 and give the conditions for different Smarandache curves to be …
Galilean space G4 and give the conditions for different Smarandache curves to be …
Family of surfaces with a common special involute and evolute curves
In this paper, we define the necessary and sufficient conditions for a parametric surface on
which both the involute and evolute of any given curve lie to be geodesic, asymptotic and …
which both the involute and evolute of any given curve lie to be geodesic, asymptotic and …
[PDF][PDF] Surface family with a common asymptotic curve in Minkowski 3-space
In this paper, we express surfaces parametrically through a given spacelike (timelike)
asymptotic curve using the Frenet frame of the curve in Minkowski 3-space. Necessary and …
asymptotic curve using the Frenet frame of the curve in Minkowski 3-space. Necessary and …
Family of Surfaces with a Common Bertrand D-Curve as Isogeodesic, Isoasymptotic and Line of Curvature.
In this paper, we establish the necessary and sufficient conditions to parameterize a surface
family on which the Bertrand D-partner of any given curve lies as isogeodesic, isoasymptotic …
family on which the Bertrand D-partner of any given curve lies as isogeodesic, isoasymptotic …
Hypersurface families with Smarandache curves in Galilean 4-space
In this paper, we study the hypersurface families with Smarandache curves in 4-dimensional
Galilean space G4 and give the conditions for different Smarandache curves to be …
Galilean space G4 and give the conditions for different Smarandache curves to be …
Surface Family With A Common Bertrand B-Isoasymptotic Curve
This study consists of four sections. In the first section, objective of the study and background
are given. Second section is devoted to basic definitions and theorems related to 3 …
are given. Second section is devoted to basic definitions and theorems related to 3 …
[PDF][PDF] Family of surfaces with a common alternative partner curve as asymptotic, geodesic and curvature line
In this study, the necessary and sufficient conditions are provided to form a surface family on
which the alternative partner of any given curve lies as isogeodesic, isoasymptotic and …
which the alternative partner of any given curve lies as isogeodesic, isoasymptotic and …
(R1499) Family of Surfaces with a Common Bertrand D-Curve as Isogeodesic, Isoasymptotic and Line of Curvature
In this paper, we establish the necessary and sufficient conditions to parameterize a surface
family on which the Bertrand D-partner of any given curve lies as isogeodesic, isoasymptotic …
family on which the Bertrand D-partner of any given curve lies as isogeodesic, isoasymptotic …
NEW PARAMETRIC REPRESENTATION OF A SURFACE FAMILY WITH COMMON SMARANDACHE ASYMPTOTIC BY USING BISHOP FRAME
MT SARIAYDIN, V ASIL - International Conference on Pure …, 2015 - acikerisim.bartin.edu.tr
In this paper, we study common smarandache asymptotic curves on a surface in the
Euclidean 3-space. By utilizing the Bishop frame, the surface family can be expressed as a …
Euclidean 3-space. By utilizing the Bishop frame, the surface family can be expressed as a …