scholarly journals Some Results and Characterizations for Mannheim Offsets of the Ruled Surfaces

2016 ◽  
Vol 34 (1) ◽  
pp. 85-98 ◽  
Author(s):  
Mehmet Önder ◽  
H. Hüseyin Uğurlu
Keyword(s):  
Ruled Surfaces ◽  
Developable Surface ◽  
Integral Invariants ◽  
Offset Surfaces ◽  
Spherical Images ◽  
Mannheim Offset

In this study, we give the dual characterizations of Mannheim offsets of ruled surfaces in terms of their integral invariants and obtain a new characterization of the Mannheim offsets of developable surface, i.e., we show that the striction lines of developable Mannheim offset surfaces are Mannheim partner curves. Furthermore, we obtain the relationships between the area of projections of spherical images for Mannheim offsets of ruled surfaces and their integral invariants.

On the invariants of Mannheim offsets of timelike ruled surfaces with spacelike rulings

2015 ◽  
Vol 08 (01) ◽  
pp. 1550009 ◽  
Author(s):  
Mehmet Önder ◽  
H. Hüseyin Uğurlu
Keyword(s):  
Ruled Surface ◽  
Ruled Surfaces ◽  
Lorentzian Space ◽  
Integral Invariants ◽  
Timelike Ruled Surface ◽  
Spherical Images

In this paper, we give the characterizations for Mannheim offsets of timelike ruled surfaces with spacelike rulings in dual Lorentzian space [Formula: see text]. We obtain the relations between terms of their integral invariants and also we give new characterization for the Mannheim offsets of developable timelike ruled surface. Moreover, we find relations between the area of projections of spherical images for Mannheim offsets of timelike ruled surfaces and their integral invariants.

scholarly journals Characterization of affine ruled surfaces

1997 ◽  
Vol 39 (1) ◽  
pp. 17-20 ◽  
Author(s):  
Włodzimierz Jelonek
Keyword(s):  
Shape Operator ◽  
Ruled Surfaces ◽  
Affine Sphere ◽  
Affine Surface ◽  
Codazzi Tensor ◽  
Difference Tensor ◽  
The Difference ◽  
In The Beginning ◽  
Affine Metric

The aim of this paper is to give certain conditions characterizing ruled affine surfaces in terms of the Blaschke structure (∇, h, S) induced on a surface (M, f) in ℝ3. The investigation of affine ruled surfaces was started by W. Blaschke in the beginning of our century (see [1]). The description of affine ruled surfaces can be also found in the book [11], [3] and [7]. Ruled extremal surfaces are described in [9]. We show in the present paper that a shape operator S is a Codazzi tensor with respect to the Levi-Civita connection ∇ of affine metric h if and only if (M, f) is an affine sphere or a ruled surface. Affine surfaces with ∇S = 0 are described in [2] (see also [4]). We also show that a surface which is not an affine sphere is ruled iff im(S - HI) =ker(S - HI) and ket(S - HI) ⊂ ker dH. Finally we prove that an affine surface with indefinite affine metric is a ruled affine sphere if and only if the difference tensor K is a Codazzi tensor with respect to ∇.

scholarly journals Some Characteristic Properties of Parallelz-Equidistant Ruled Surfaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Engin As ◽  
Süleyman Şenyurt
Keyword(s):  
Ruled Surfaces ◽  
Integral Invariants ◽  
Normal Vectors ◽  
The Relationship

Some characteristic properties of two ruled surfaces whose principal normal vectors are parallel along their striction curves inE3are examined by assuming that the distance between two central planes at suitable points is constant,E3. In case of which two ruled surfaces are close, the relationship between the integral invariants of this ruled surfaces is computed.

On the kinematic interpretation of timelike ruled surfaces

2015 ◽  
Vol 12 (10) ◽  
pp. 1550127 ◽  
Author(s):  
Mehmet Önder ◽  
Zehra Ekinci
Keyword(s):  
Ruled Surface ◽  
Ruled Surfaces ◽  
Reference Surface ◽  
Screw Axis ◽  
Lorentzian Space ◽  
Timelike Ruled Surface ◽  
Instantaneous Screw Axis ◽  
Associated Surfaces ◽  
Instantaneous Screw ◽  
Mannheim Offset

Timelike ruled surfaces are studied in dual Lorentzian space [Formula: see text] by considering E. Study Mapping and Blaschke frame. A reference timelike ruled surface is considered and associated surfaces are defined. First, it is shown that the surface generated by the instantaneous screw axis (ISA) is a Mannheim offset of reference surface. Later, the kinematic interpretations between these surfaces are introduced by means of Blaschke invariants.

scholarly journals Mannheim Offsets of Ruled Surfaces

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Keziban Orbay ◽  
Emin Kasap ◽  
İsmail Aydemir
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Geodesic Curvature ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Arc Length ◽  
Spherical Indicatrix ◽  
Constant Distance ◽  
Mannheim Offset ◽  
Three Dimensional Space

In a recent works Liu and Wang (2008; 2007) study the Mannheim partner curves in the three dimensional space. In this paper, we extend the theory of the Mannheim curves to ruled surfaces and define two ruled surfaces which are offset in the sense of Mannheim. It is shown that, every developable ruled surface have a Mannheim offset if and only if an equation should be satisfied between the geodesic curvature and the arc-length of spherical indicatrix of it. Moreover, we obtain that the Mannheim offset of developable ruled surface is constant distance from it. Finally, examples are also given.

scholarly journals Characterization of rational ruled surfaces

2014 ◽  
Vol 63 ◽  
pp. 21-45 ◽  
Author(s):  
Li-Yong Shen ◽  
Sonia Pérez-Díaz
Keyword(s):  
Ruled Surfaces

scholarly journals Timelike Sweeping Surfaces According to Type-2 Bishop Frame in Minkowski 3–space

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Ruled Surfaces ◽  
Developable Surface ◽  
Bishop Frame ◽  
Tangential Surface ◽  
Necessary And Sufficient

In this paper, we express timelike sweeping surfaces using rotation minimizing frames in Minkowski 3–Space E3 1 . Necessary and sufficient conditions for timelike sweeping surfaces to be developable ruled surfaces are derived. Using these, we analyze the conditions when the resulting timelike developable surface is a cylinder, cone or tangential surface.

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