INVOLUTE-EVOLUTE CURVES ACCORDING TO MODIFIED ORTHOGONAL FRAME

2021 ◽  
Vol 21 (2) ◽  
pp. 385-394
Author(s):  
AYŞE ZEYNEP AZAK
Keyword(s):  
Euclidean Space ◽  
Curvature And Torsion ◽  
Orthogonal Pairs ◽  
Orthogonal Frame ◽  
Zero Points

In this paper, the involute-evolute curve concept has been defined according to two type modified orthogonal frames at non-zero points of curvature and torsion in the Euclidean space E^3 , respectively. Later, the characteristic theorems related to the distance between the corresponding points of these curves have been given. Besides, the relations have been found between the curvatures and also torsions of the two type the involute-evolute modified orthogonal pairs.

scholarly journals Differential geometry of intersection curve of two surfaces

2009 ◽  
Vol 50 ◽  
Author(s):  
Kazimieras Navickis
Keyword(s):  
Differential Geometry ◽  
Euclidean Space ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Intersection Curve ◽  
Curvature And Torsion

In this this article the differential geometry of intersection curve of two surfaces in the three dimensional euclidean space is considered.In case, curvature and torsion formulas for such curve are defined.

scholarly journals Some integral curves with a new frame

2020 ◽  
Vol 18 (1) ◽  
pp. 1332-1341
Author(s):  
İlkay Arslan Güven
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Integral Curves ◽  
Curvature And Torsion

Abstract In this paper, some new integral curves are defined in three-dimensional Euclidean space by using a new frame of a polynomial spatial curve. The Frenet vectors, curvature and torsion of these curves are obtained by means of new frame and curvatures. We give the characterizations and properties of these integral curves under which conditions they are general helix. Also, the relationships between these curves in terms of being some kinds of associated curves are introduced. Finally, an example is illustrated.

scholarly journals Differential geometry of intersection curve of two surfaces

2008 ◽  
Vol 48 ◽  
Author(s):  
Kazimieras Navickis
Keyword(s):  
Differential Geometry ◽  
Euclidean Space ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Intersection Curve ◽  
Curvature And Torsion

In this this article the differential geometry of intersection curve of two surfaces in the three dimensional euclidean space is considered. In case, curvature and torsion formulas for such curve are defined.

scholarly journals Generated Surfaces via Inextensible Flows of Curves inR3

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Rawya A. Hussien ◽  
Samah G. Mohamed
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space ◽  
Geometric Properties ◽  
3 Dimensional ◽  
Inextensible Flows ◽  
Curvature And Torsion

We study the inextensible flows of curves in 3-dimensional Euclidean spaceR3. The main purpose of this paper is constructing and plotting the surfaces that are generated from the motion of inextensible curves inR3. Also, we study some geometric properties of those surfaces. We give some examples about the inextensible flows of curves inR3and we determine the curves from their intrinsic equations (curvature and torsion). Finally, we determine and plot the surfaces that are generated by the motion of those curves by using Mathematica 7.

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 Application of the geometry of curves in Euclidean space

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1029-1036 ◽  
Author(s):  
Kostadin Trencevski
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space ◽  
Lorentz Transformations ◽  
3 Dimensional ◽  
Essential Properties ◽  
Curvature And Torsion

In this article the so called induced spin velocities are studied, and it is an improvement of the paper [13] using the geometry of curves in 3-dimensional Euclidean space. Some essential properties of them are given, and they are rather different than the ordinary velocities. Indeed, the induced spin velocities are non-inertial and instead of the Lorentz transformations for them the Galilean transformations should be used. The induced spin velocity is derived in terms of the curvature and torsion of the trajectory. Two applications of the induced spin velocities are studied.

Symplectic capacities

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Euclidean Space ◽  
Generating Functions ◽  
Weinstein Conjecture ◽  
Finite Dimensional ◽  
Hofer Metric

This chapter returns to the problems which were formulated in Chapter 1, namely the Weinstein conjecture, the nonsqueezing theorem, and symplectic rigidity. These questions are all related to the existence and properties of symplectic capacities. The chapter begins by discussing some of the consequences which follow from the existence of capacities. In particular, it establishes symplectic rigidity and discusses the relation between capacities and the Hofer metric on the group of Hamiltonian symplectomorphisms. The chapter then introduces the Hofer–Zehnder capacity, and shows that its existence gives rise to a proof of the Weinstein conjecture for hypersurfaces of Euclidean space. The last section contains a proof that the Hofer–Zehnder capacity satisfies the required axioms. This proof translates the Hofer–Zehnder variational argument into the setting of (finite-dimensional) generating functions.

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