scholarly journals The integral invariants of parallel timelike ruled surfaces

2012 ◽  
Vol 393 (1) ◽  
pp. 97-107
Author(s):  
Cumali Ekici ◽  
A. Ceylan Çöken
Keyword(s):  
Ruled Surfaces ◽  
Integral Invariants

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.

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.

Integral invariants in chemical kinetics

1991 ◽  
Vol 44 (2) ◽  
pp. 409-414
Author(s):  
L. Ropolyi ◽  
P. Réti
Keyword(s):  
Chemical Kinetics ◽  
Integral Invariants

The surfaces whose prime-sections contain a

1934 ◽  
Vol 30 (2) ◽  
pp. 170-177 ◽  
Author(s):  
J. Bronowski
Keyword(s):  
Hyperelliptic Curves ◽  
Ruled Surfaces ◽  
Minimum Order ◽  
Rational Surfaces ◽  
Pencil Of Conics

The surfaces whose prime-sections are hyperelliptic curves of genus p have been classified by G. Castelnuovo. If p > 1, they are the surfaces which contain a (rational) pencil of conics, which traces the on the prime-sections. Thus, if we exclude ruled surfaces, they are rational surfaces. The supernormal surfaces are of order 4p + 4 and lie in space [3p + 5]. The minimum directrix curve to the pencil of conics—that is, the curve of minimum order which meets each conic in one point—may be of any order k, where 0 ≤ k ≤ p + 1. The prime-sections of these surfaces are conveniently represented on the normal rational ruled surfaces, either by quadric sections, or by quadric sections residual to a generator, according as k is even or odd.

The integral invariants of n gyrostats

1990 ◽  
Vol 17 (2) ◽  
pp. 75-80
Author(s):  
A.G. Mavraganis
Keyword(s):  
Integral Invariants
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