On calculation of the pitch and angle of pitch of a closed ruled surface of dimension ( k  + 1) using a rotation minimizing frame in Euclidean space ℝn

2021 ◽  
Author(s):  
Özgür Keskin ◽  
Ayşe Altin ◽  
Faik Nejat Ekmekci ◽  
Yusuf Yayli
Keyword(s):  
Euclidean Space ◽  
Ruled Surface ◽  
Rotation Minimizing Frame

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 BELTRAMI-EULER FORMULAS OF GENERALIZED SEMI-RULED SURFACE IN SEMI EUCLIDEAN SPACE

2015 ◽  
Vol 8 (1) ◽  
pp. 105-115
Author(s):  
Mahmut AKYİĞİT ◽  
Soley ERSOY ◽  
Murat TOSUN
Keyword(s):  
Euclidean Space ◽  
Ruled Surface

scholarly journals Offset Ruled Surface in Euclidean Space with Density

2021 ◽  
Vol 29 (1) ◽  
pp. 219-233
Author(s):  
Neslihan Ulucan ◽  
Mahmut Akyigit
Keyword(s):  
Euclidean Space ◽  
Gaussian Curvature ◽  
Mean Curvature ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Surfaces In Euclidean Space ◽  
The Mean

Abstract In this paper, offset ruled surfaces in these spaces are defined by using the geometry of ruled surfaces in Euclidean space with density. The mean curvature and Gaussian curvature of these surfaces are studied. In addition, the relationships between the mean curvature and mean curvature with density, and the Gaussian curvature and the Gaussian curvature with density of the offset ruled surfaces in E 3 with density e z and e − x 2− y 2 are given.

scholarly journals Ruled surfaces of finite type

1990 ◽  
Vol 42 (3) ◽  
pp. 447-453 ◽  
Author(s):  
Bang-Yen Chen ◽  
Franki Dillen ◽  
Leopold Verstraelen ◽  
Luc Vrancken
Keyword(s):  
Euclidean Space ◽  
Finite Type ◽  
Ruled Surface ◽  
Ruled Surfaces

We show that a ruled surface of finite type in a Euclidean space is a cylinder on a curve of finite type or a helicoid in Euclidean 3-space.

scholarly journals Singularities of Non-Developable Surfaces in Three-Dimensional Euclidean Space

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1106
Author(s):  
Jie Huang ◽  
Donghe Pei
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
Singularity Theory ◽  
Structure Functions ◽  
Ruled Surface ◽  
Singular Points ◽  
Dimensional Euclidean Space ◽  
Smooth Curves ◽  
Developable Surfaces

We study the singularity on principal normal and binormal surfaces generated by smooth curves with singular points in the Euclidean 3-space. We discover the existence of singular points on such binormal surfaces and study these singularities by the method of singularity theory. By using structure functions, we can characterize the ruled surface generated by special curves.

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.

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.

ANTI-SELF-DUAL SOLUTIONS OF THE YANG-MILLS EQUATIONS IN 4n DIMENSIONS

1992 ◽  
Vol 07 (23) ◽  
pp. 2077-2085 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Scalar Field ◽  
Euclidean Space ◽  
Lie Algebra ◽  
Linear Equations ◽  
Dual Solutions ◽  
Gauge Fields ◽  
System Of Equations ◽  
Semisimple Lie Algebra ◽  
Yang Mills ◽  
Self Duality

The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.

Sign in / Sign up

Export Citation Format

Share Document