In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generate...

By using the Darboux frame |?, ?, ?| of a non-null curve lying on timelike surface in Minkowski 3-space, where ? is unit tangent vector curve, spacelike normal field restricted to and = ?? we define relatively normal-slant helices as curves satisfying condition that scalar product fixed spanning their axis non-constant constant. We give necessary sufficient conditions for be helices. consider s...

In this paper, an isomorphism between unit dual sphere, DS2, and the subset of tangent bundle 2-sphere, T?M, is represented. According to E. Study mapping, a ruled surface in IR3 corresponds each curve on DS2. Through isomorphism, new forms surfaces called slant were introduced. Moreover, conditions for these be given. Finally, unique ?q?,?h? ?? corresponded striction natural lift T?M.

Abstract In this study, we define the generalized normal ruled surface of a curve in Euclidean 3-space E 3 . We study geometry such surfaces by calculating Gaussian and mean curvatures to determine when is flat or minimal (equivalently, helicoid). examine conditions for curves lying on be asymptotic curves, geodesics lines curvature. Finally, obtain Frenet vectors get some relations with helice...

for the first time in the minkowski space, an rn 1 time-like complementary ruled surface isdescribed and relations are given connected with an asymptotic and tangential bundle of the time-likecomplementary ruled surface. furthermore, theorems are given related to edge space, central space andcentral ruled surface of this complementary ruled surface.

Stereoscopic slant contrast is an apparent slant induced in a stereoscopically frontal plane surface (the test) opposite in direction to the specified stereoscopic slant of a neighbouring surface (the inducer). Test surfaces offset from the inducer in a direction collinear with the axis of slant (twist) show more contrast than those offset in a direction orthogonal to the axis of slant (hinge)....

in this paper, the lorentzian version of beltrami-euler formula is investigated in 1n . initially,the first fundamental form and the metric coefficients of generalized timelike ruled surface are calculated and by the help of the christoffel symbols, riemann-christoffel curvatures are obtained. thus, the curvatures of spacelike and timelike tangential sections of generalized timelike ruled surf...

in this study, a generalization of the theory of involute-evolute curves is presented for ruledsurfaces based on line geometry. using lines instead of points, two ruled surfaces which are offset in the senseof involute-evolute are defined. moreover, the found results are clarified using computer-aided examples

Gradients of absolute binocular disparity across a slanted surface are often considered the basis for stereoscopic slant perception. However, perceived stereo slant around a vertical axis is usually slow and significantly under-estimated for isolated surfaces. Perceived slant is enhanced when surrounding surfaces provide a relative disparity gradient or depth step at the edges of the slanted su...