A New Approach to Mannheim Curve in Euclidean 3-Space

Dimensional Euclidean Space ◽

New Approach ◽

3 Dimensional ◽

Mannheim Curve ◽

In this article, a new approach is given for Mannheim curves in 3-dimensional Euclidean space. Thanks to this approach, the necessary and sufficient conditions including the known results have been obtained for a curve to be Mannheim curve in E³. In addition, related examples and graphs are given by showing that there can be Mannheim curves in Salkowski or anti-Salkowski curves as well as giving Mannheim mate curves, which are not in literature. Finally, the Mannheim partner curves are characterized in E³.

Generalized Timelike Mannheim Curves in Minkowski Space-Time

Mathematical Problems in Engineering ◽

10.1155/2011/539378 ◽

2011 ◽

Vol 2011 ◽

pp. 1-19 ◽

Cited By ~ 3

Author(s):

M. Akyig~it ◽

S. Ersoy ◽

İ. Özgür ◽

M. Tosun

Keyword(s):

Minkowski Space ◽

Sufficient Conditions ◽

Space Time ◽

Minkowski Space Time ◽

Mannheim Curve ◽

Definition Of ◽

We give the definition of generalized timelike Mannheim curve in Minkowski space-time . The necessary and sufficient conditions for the generalized timelike Mannheim curve are obtained. We show some characterizations of generalized Mannheim curve.

22nd Biennial Mechanisms Conference: Robotics, Spatial Mechanisms, and Mechanical Systems ◽

A New Approach to Type Synthesis of Spatial Robotic Mechanisms

10.1115/detc1992-0238 ◽

1992 ◽

Author(s):

Akhtar N. Malik ◽

D. R. Kerr

Keyword(s):

Robot Manipulators ◽

Sufficient Conditions ◽

Type Synthesis ◽

End Effector ◽

New Approach ◽

Parallel Platform ◽

Abstract This paper presents a new approach for carrying out the type synthesis of spatial parallel platform-type mechanisms, used as robot manipulators. It takes into account the total mobility of the system and the partial mobility of its sub-mechanisms. The paper also provides the necessary and sufficient conditions for the mechanisms to function with specified end-effector freedoms, which are described in two theorems. The total number of possible mechanisms with given mobility and structure are tabulated. The work is based on a modified Grübler mobility criterion and also on the consideration of kinematic restraints.

Characterization of Extreme Points of Multi-Stochastic Tensors

Computational Methods in Applied Mathematics ◽

10.1515/cmam-2016-0005 ◽

2016 ◽

Vol 16 (3) ◽

pp. 459-474 ◽

Cited By ~ 8

Author(s):

Rihuan Ke ◽

Wen Li ◽

Mingqing Xiao

Keyword(s):

Operation Research ◽

Convex Combination ◽

Sufficient Conditions ◽

Extreme Points ◽

Stochastic Matrices ◽

Third Order ◽

New Approach ◽

3 Dimensional ◽

AbstractStochastic matrices play an important role in the study of probability theory and statistics, and are often used in a variety of modeling problems in economics, biology and operation research. Recently, the study of tensors and their applications became a hot topic in numerical analysis and optimization. In this paper, we focus on studying stochastic tensors and, in particular, we study the extreme points of a set of multi-stochastic tensors. Two necessary and sufficient conditions for a multi-stochastic tensor to be an extreme point are established. These conditions characterize the “generators” of multi-stochastic tensors. An algorithm to search the convex combination of extreme points for an arbitrary given multi-stochastic tensor is developed. Based on our obtained results, some expression properties for third-order and n-dimensional multi-stochastic tensors (${n=3}$ and 4) are derived, and all extreme points of 3-dimensional and 4-dimensional triply-stochastic tensors can be produced in a simple way. As an application, a new approach for the partially filled square problem under the framework of multi-stochastic tensors is given.

On η-Einstein Trans-Sasakian Manifolds

Annals of the Alexandru Ioan Cuza University - Mathematics ◽

10.2478/v10157-011-0036-x ◽

2011 ◽

Vol 57 (2) ◽

pp. 417-440

Author(s):

Falleh Al-Solamy ◽

Jeong-Sik Kim ◽

Mukut Tripathi

Keyword(s):

Vector Field ◽

Sufficient Conditions ◽

Sasakian Manifold ◽

Sasakian Manifolds ◽

Contact Metric Manifold ◽

Almost Contact Metric Manifold ◽

3 Dimensional ◽

Almost Contact Metric ◽

On η-Einstein Trans-Sasakian ManifoldsA systematic study of η-Einstein trans-Sasakian manifold is performed. We find eight necessary and sufficient conditions for the structure vector field ζ of a trans-Sasakian manifold to be an eigenvector field of the Ricci operator. We show that for a 3-dimensional almost contact metric manifold (M,φ, ζ, η, g), the conditions of being normal, trans-K-contact, trans-Sasakian are all equivalent to ∇ζ ∘ φ = φ ∘ ∇ζ. In particular, the conditions of being quasi-Sasakian, normal with 0 = 2β = divζ, trans-K-contact of type (α, 0), trans-Sasakian of type (α, 0), andC6-class are all equivalent to ∇ ζ = -αφ, where 2α = Trace(φ∇ζ). In last, we give fifteen necessary and sufficient conditions for a 3-dimensional trans-Sasakian manifold to be η-Einstein.

Semi-symmetry of δ(2,2) Chen ideal submanifolds

Filomat ◽

10.2298/fil1503393p ◽

2015 ◽

Vol 29 (3) ◽

pp. 393-400

Author(s):

Anica Pantic ◽

Miroslava Petrovic-Torgaseva

Keyword(s):

Euclidean Space ◽

Sufficient Conditions ◽

In this paper we discuss ?(2,2) Chen ideal submanifolds M4 in the Euclidean space E6, and we find the necessary and sufficient conditions under which such a submanifold M4 is semi-symmetric, i.e. it satisfies the condition R(X,Y)? R = 0.

Smooth Finite Dimensional Embeddings

Canadian Journal of Mathematics ◽

10.4153/cjm-1999-027-1 ◽

1999 ◽

Vol 51 (3) ◽

pp. 585-615 ◽

Cited By ~ 2

Author(s):

R. Mansfield ◽

H. Movahedi-Lankarani ◽

R. Wells

Keyword(s):

Hilbert Space ◽

Euclidean Space ◽

Compact Subset ◽

Structure Theorem ◽

Sufficient Conditions ◽

Dimensional Euclidean Space ◽

Locally Compact ◽

Finite Dimensional ◽

Necessary And Sufficient ◽

Compact Subsets

AbstractWe give necessary and sufficient conditions for a norm-compact subset of a Hilbert space to admit a C1 embedding into a finite dimensional Euclidean space. Using quasibundles, we prove a structure theorem saying that the stratum of n-dimensional points is contained in an n-dimensional C1 submanifold of the ambient Hilbert space. This work sharpens and extends earlier results of G. Glaeser on paratingents. As byproducts we obtain smoothing theorems for compact subsets of Hilbert space and disjunction theorems for locally compact subsets of Euclidean space.

Hypersurfaces of Euclidean Space as Gradient Ricci Solitons

Annals of the Alexandru Ioan Cuza University - Mathematics ◽

10.2478/aicu-2014-0009 ◽

2014 ◽

Vol 0 (0) ◽

Cited By ~ 1

Author(s):

Hana Al-Sodais ◽

Haila Alodan ◽

Sharief Deshmukh

Keyword(s):

Euclidean Space ◽

Sufficient Conditions ◽

Ricci Soliton ◽

Ricci Solitons ◽

Gradient Ricci Soliton ◽

Gradient Ricci Solitons ◽

Abstract In this paper we obtain some necessary and sufficient conditions for a hypersurface of a Euclidean space to be a gradient Ricci soliton. We also study the geometry of a special type of compact Ricci solitons isometrically immersed into a Euclidean space.

A new approach to canal surface with parallel transport frame

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887817500268 ◽

2017 ◽

Vol 14 (02) ◽

pp. 1750026 ◽

Cited By ~ 4

Author(s):

İlim Kiṣi ◽

Günay Öztürk

Keyword(s):

Parallel Transport ◽

Sufficient Conditions ◽

Canal Surface ◽

New Approach ◽

Canal Surfaces ◽

In the present study, we attend to the canal surfaces with the spine curve [Formula: see text] according to the parallel transport frame in Euclidean [Formula: see text]-space [Formula: see text]. We give an example of these surfaces and obtain some results about curvature conditions in [Formula: see text]. Moreover, the visualizations of projections of canal surfaces are presented. Lastly, we give the necessary and sufficient conditions for canal surfaces to become weak superconformal.

SURFACE FAMILY WITH COMMON LINE OF CURVATURE IN 3-DIMENSIONAL GALILEAN SPACE

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi2005315a ◽

2021 ◽

pp. 1315

Author(s):

Mustafa Altin ◽

İnan Ünal

Keyword(s):

Sufficient Conditions ◽

3 Dimensional ◽

Common Line ◽

Galilean Space ◽

Necessary And Sufficient ◽

Torsion Free ◽

Line Of Curvature

In this paper we study to find parametric presentation of a surface family with common line of curvature in 3-dimensional Galilean space. We obtain necessary and sufficient conditions for the curve to be a common line of curvature on this surface. We state examples to visualize our results and we obtain some results for a torsion free curve.

Some Conditions on Trans-Sasakian Manifolds to Be Homothetic to Sasakian Manifolds

Mathematics ◽

10.3390/math9161887 ◽

2021 ◽

Vol 9 (16) ◽

pp. 1887

Author(s):

Sharief Deshmukh ◽

Amira Ishan ◽

Olga Belova ◽

Suha B. Al-Shaikh

Keyword(s):

Sufficient Conditions ◽

Sasakian Manifold ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Sasakian Manifolds ◽

3 Dimensional ◽

Necessary And Sufficient ◽

Simply Connected

In this paper, we study 3-dimensional compact and connected trans-Sasakian manifolds and find necessary and sufficient conditions under which these manifolds are homothetic to Sasakian manifolds. First, four results in this paper deal with finding necessary and sufficient conditions on a compact and connected trans-Sasakian manifold to be homothetic to a compact and connected Sasakian manifold, and the fifth result deals with finding necessary and sufficient condition on a connected trans-Sasakian manifold to be homothetic to a connected Sasakian manifold. Finally, we find necessary and sufficient conditions on a compact and simply connected trans-Sasakian manifold to be homothetic to a compact and simply connected Einstein Sasakian manifold.