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.

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.

The bi-normal fields on spacelike surfaces in ℝ14

2016 ◽  
Vol 09 (03) ◽  
pp. 1650052
Author(s):  
Dang Van Cuong
Keyword(s):  
Ruled Surfaces ◽  
Spacelike Surface ◽  
Surfaces Of Revolution ◽  
Normal Field ◽  
Planar Surfaces ◽  
Spacelike Surfaces ◽  
The Relationship

A normal field [Formula: see text] on a spacelike surface in [Formula: see text] is called bi-normal if [Formula: see text], the determinant of the Weingarten map associated to [Formula: see text], is zero. In this paper, we give a criterion to check if a normal field is bi-normal. Then we study the relationship between the spacelike pseudo-planar surfaces and spacelike pseudo-umbilical surfaces. We also study the bi-normal fields on spacelike ruled surfaces and spacelike surfaces of revolution.

scholarly journals On parallel p-equidistant ruled surfaces by using mofied orthogonal frame with curvature in E³

2022 ◽  
Vol 40 ◽  
pp. 1-7
Author(s):  
Muhammed T. Sariaydin ◽  
Talat Korpinar ◽  
Vedat Asil
Keyword(s):  
Euclidean Space ◽  
Apex Angle ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Dimensional Euclidean Space ◽  
3 Dimensional ◽  
The Relationship ◽  
Orthogonal Frame

In this paper, it is investigated Ruled surfaces according to modified orthogonal frame with curvature in 3-dimensional Euclidean space. Firstly, we give apex angle, pitch and drall of closed ruled surface in E³. Then,  it characterized the relationship between these invariant of parallel p-equidistant ruled surfaces.

scholarly journals The dual spatial quaternionic expression of ruled surfaces

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 403-411
Author(s):  
Abdussamet Caliskan ◽  
Süleyman Şenyurt
Keyword(s):  
Unit Sphere ◽  
Dual Space ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Integral Invariants ◽  
Dual Expression

In this paper, the ruled surface which corresponds to a curve on dual unit sphere is rederived with the help of dual spatial quaternions. We extend the term of dual expression of ruled surface using dual spatial quaternionic method. The correspondences in dual space of closed ruled surfaces are quaternionically expressed. As a consequence, the integral invariants of these surfaces and the relationships between these invariants are shown

scholarly journals The quaternionic expression of ruled surfaces

Filomat ◽  
2018 ◽  
Vol 32 (16) ◽  
pp. 5753-5766 ◽  
Author(s):  
Süleyman Şenyurt ◽  
Abdussamet Çalışkan
Keyword(s):  
Ruled Surface ◽  
Distribution Parameter ◽  
Ruled Surfaces ◽  
Integral Invariants

In this paper, firstly, the ruled surface is expressed as a spatial quaternionic. Also, the spatial quaternionic definitions of the Striction curve, the distribution parameter, angle of pitch and the pitch are given. Finally, integral invariants of the closed spatial quaternionic ruled surfaces drawn by the motion of the Frenet vectors {t,n1,n2} belonging to the spatial quaternionic curve ? are calculated.

Interstellar gas in the central region of the Galaxy

1967 ◽  
Vol 31 ◽  
pp. 239-251 ◽  
Author(s):  
F. J. Kerr
Keyword(s):  
Central Region ◽  
Galactic Plane ◽  
Neutral Hydrogen ◽  
Continuum Emission ◽  
Galactic Centre ◽  
Interstellar Gas ◽  
Hydrogen Recombination ◽  
The Galaxy ◽  
Centre Region ◽  
The Relationship

A review is given of information on the galactic-centre region obtained from recent observations of the 21-cm line from neutral hydrogen, the 18-cm group of OH lines, a hydrogen recombination line at 6 cm wavelength, and the continuum emission from ionized hydrogen.Both inward and outward motions are important in this region, in addition to rotation. Several types of observation indicate the presence of material in features inclined to the galactic plane. The relationship between the H and OH concentrations is not yet clear, but a rough picture of the central region can be proposed.

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