149 research outputs found
Dual Darboux Frame of a Timelike Ruled Surface and Darboux Approach to Mannheim Offsets of Timelike Ruled Surfaces
In this paper, we introduce the dual geodesic trihedron (dual Darboux frame)
of a timelike ruled surface. By the aid of the E. Study Mapping, we consider
timelike ruled surfaces as dual hyperbolic spherical curves and define the
Mannheim offsets of timelike ruled surfaces by means of dual Darboux frame. We
obtain the relationships between invariants of Mannheim timelike surface
offsets. Furthermore, we give the conditions for these surface offsets to be
developable.Comment: 12 page
On the Developable Mannheim Offsets of Spacelike Ruled Surfaces
In this paper, using the classifications of timelike and spacelike ruled
surfaces, we define and study the Mannheim offsets of spacelike ruled surfaces
in Minkowski 3-space. We give the conditions for spacelike offset surfaces to
be developable.Comment: 10 pages. arXiv admin note: substantial text overlap with
arXiv:0906.2077, arXiv:1007.2041; and overlap with arXiv:1001.4683 by other
author
Dual Darboux Frame of a Spacelike Ruled Surface and Darboux Approach to Mannheim Offsets of Spacelike Ruled Surfaces
In this paper, we define dual geodesic trihedron(dual Darboux frame) of a
spacelike ruled surface. Then, we study Mannheim offsets of spacelike ruled
surfaces in dual Lorentzian space by considering the E. Study Mapping. We
represent spacelike ruled surfaces by dual Lorentzian unit spherical curves and
define Mannheim offsets of the spacelike ruled surfaces by means of dual
Darboux frame. We obtain relationships between the invariants of Mannheim
spacelike offset surfaces and offset angle, offset distance. Furthermore, we
give conditions for these surface offsets to be developable.Comment: 13 pages. arXiv admin note: substantial text overlap with
arXiv:1108.607
Mannheim Partner D-Curves in Minkowski 3-space
In this paper, we give the definition, different types and characterizations
of Mannheim partner D-curves in Minkowski 3-space. We find the relations
between the geodesic curvatures, the normal curvatures and the geodesic
torsions of these associated curves. Furthermore, we show that the definition
and the characterizations of Mannheim partner D-curves include those of
Mannheim partner curves in some special cases in Minkowski 3-space.Comment: 15 pages
Mannheim Partner D-Curves in Euclidean 3-space
In this paper we consider the idea of Mannheim partner curves for curves
lying on surfaces and by considering the Darboux frames of them we define these
curves as Mannheim partner D-curves and give the characterizations for these
curves. We also find the relations between the geodesic curvatures, the normal
curvatures and the geodesic torsions of these associated curves. Furthermore,
we show that the definition and the characterizations of Mannheim partner
D-curves include those of Mannheim partner curves in some special cases.Comment: 10 page
Bertrand Partner D-Curves in Euclidean 3-space
In this paper we consider the idea of Bertrand curves for curves lying on
surfaces and by considering the Darboux frames of them we define these curves
as Bertrand D-curves and give the characterizations for these curves. We also
find the relations between the geodesic curvatures, the normal curvatures and
the geodesic torsions of these associated curves. Furthermore, we show that the
definition and the characterizations of Bertrand D-curves include those of
Bertrand curves in some special cases.Comment: 10 pages
Normal and Spherical Curves in Dual Space
In this paper, we give definitions and characterizations of normal and
spherical curves in the dual space. We show that normal curves are also
spherical curves in D^3.Comment: 9 page
On the Developable Mannheim Offsets of Timelike Ruled Surfaces
In this paper, using the classifications of timelike and spacelike ruled
surfaces, we study the Mannheim offsets of timelike ruled surfaces in Minkowski
3-space. Firstly, we define the Mannheim offsets of a timelike ruled surface by
considering the Lorentzian casual character of the offset surface. We obtain
that the Mannheim offsets of a timelike ruled surface may be timelike or
spacelike. Furthermore, we characterize the developable of Mannheim offset of a
timelike ruled surface by the derivative of the conical curvature of the
directing cone.Comment: 11 pages. arXiv admin note: substantial text overlap with
arXiv:0906.4660, arXiv:1007.204
Some Results and Characterizations for Mannheim Offsets of the Ruled Surfaces
In this study, we give the dual characterizations of Mannheim offsets of the
ruled surface in terms of their integral invariants and the new
characterization of the Mannheim offsets of developable surface. Furthermore,
we obtain the relationships between the area of projections of spherical images
for Mannheim offsets of ruled surfaces and their integral invariants.Comment: 12 page
Dual Smarandache Curves and Smarandache Ruled Surfaces
In this paper, by considering dual geodesic trihedron (dual Darboux frame) we
define dual Smarandache curves lying fully on dual unit sphere S^2 and
corresponding to ruled surfaces. We obtain the relationships between the
elements of curvature of dual spherical curve (ruled surface) x(s) and its dual
Smarandache curve (Smarandache ruled surface) x1(s) and we give an example for
dual Smarandache curves of a dual spherical curve.Comment: 18 Pages, 5 figure
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