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 O. Bonnet III-isometry of surfaces in three dimensional Euclidean space

1990 ◽  
Vol 49 (1) ◽  
pp. 90-110 ◽  
Author(s):  
Wenmao Yang
Keyword(s):  
Euclidean Space ◽  
Gaussian Curvature ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Surfaces Of Revolution ◽  
Principal Curvatures ◽  
Constant Gaussian Curvature ◽  
Geometric Properties ◽  
3 Dimensional ◽  
The Third

AbstractIn this paper we consider O. Bonnet III-isometry (or BIII-isometry) of surfaces in 3-dimensional Euclidean space E3 Suppose a map F: M → M* is a diffeomorphism, and F* (III*) = III, ki(m) = k*i (m*), i = 1, 2, where m ∈ M, m* ∈ M*, m* = F (m), ki and k*i are the principal curvatures of surfaces M and M* at the points m and m*, respectively, III and III* are the third fundmental forms of M and M*, respectively. In this case, we call F an O. Bonnet III-isometry from M to M*. O. Bonnet I-isometries were considered in references [1]-[5].We distinguish three cases about BIII-surfaces, which admits a non-trivial BIII-ismetry. We obtain some geometric properties of BIII-surfaces and BIII-isometries in these three cases; see Theorems 1, 2, 3 (in Section 2). We study some special BIII-surfaces: the minimal BIII-surfaces; BIII-surfaces of revolution; and BIII-surfaces with constant Gaussian curvature; see Theorems 4, 5, 6 (in Section 3).

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.

scholarly journals CURVES ON RULED SURFACES UNDER INFINITESIMAL BENDING

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Marija Najdanović ◽  
Miroslav Maksimović ◽  
Ljubica Velimirović
Keyword(s):  
Euclidean Space ◽  
Ruled Surfaces ◽  
Dimensional Euclidean Space ◽  
Hyperbolic Paraboloid ◽  
3 Dimensional ◽  
Infinitesimal Bending

Infinitesimal bending of curves lying with a given precision on ruled surfaces in 3-dimensional Euclidean space is studied. In particular, the bending of curves on the cylinder, the hyperbolic paraboloid and the helicoid are considered and appropriate bending fields are found. Some examples are graphically presented.

scholarly journals On Various Definitions of Capacity and Related Notions

1967 ◽  
Vol 30 ◽  
pp. 121-127 ◽  
Author(s):  
Makoto Ohtsuka
Keyword(s):  
Euclidean Space ◽  
Positive Charge ◽  
Dimensional Euclidean Space ◽  
3 Dimensional ◽  
Electric Capacity ◽  
De La Vallée Poussin

The electric capacity of a conductor in the 3-dimensional euclidean space is defined as the ratio of a positive charge given to the conductor and the potential on its surface. The notion of capacity was defined mathematically first by N. Wiener [7] and developed by C. de la Vallée Poussin, O. Frostman and others. For the history we refer to Frostman’s thesis [2]. Recently studies were made on different definitions of capacity and related notions. We refer to M. Ohtsuka [4] and G. Choquet [1], for instance. In the present paper we shall investigate further some relations among various kinds of capacity and related notions. A part of the results was announced in a lecture of the author in 1962.

scholarly journals Surfaces of Finite III-type

2021 ◽  
Vol 15 ◽  
pp. 190-194
Author(s):  
Hassan Al-Zoubi
Keyword(s):  
Euclidean Space ◽  
Fundamental Form ◽  
Principal Curvature ◽  
Gauss Curvature ◽  
Dimensional Euclidean Space ◽  
Surfaces Of Revolution ◽  
3 Dimensional ◽  
The Third ◽  
Third Fundamental Form ◽  
Special Case

In this paper, we consider surfaces of revolution in the 3-dimensional Euclidean space E3 with nonvanishing Gauss curvature. We introduce the finite Chen type surfaces with respect to the third fundamental form of the surface. We present a special case of this family of surfaces of revolution in E3, namely, surfaces of revolution with R is constant, where R denotes the sum of the radii of the principal curvature of a surface.

scholarly journals On the second Gaussian curvature of ruled surfaces in Euclidean $3$-space

2006 ◽  
Vol 37 (3) ◽  
pp. 221-226 ◽  
Author(s):  
Dae Won Yoon
Keyword(s):  
Euclidean Space ◽  
Gaussian Curvature ◽  
Mean Curvature ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Dimensional Euclidean Space ◽  
3 Dimensional ◽  
The Mean ◽  
Second Gaussian Curvature

In this paper, we mainly investigate non developable ruled surface in a 3-dimensional Euclidean space satisfying the equation $K_{II} = KH$ along each ruling, where $K$ is the Gaussian curvature, $H$ is the mean curvature and $K_{II}$ is the second Gaussian curvature.

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.

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