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Sep 22, 2013
09/13

by
Ahmad T Ali

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In this paper, position vector of a spacelike general helix with respect to standard frame in Minkowski space E$^3_1$ are studied in terms of Frenet equations. First, a vector differential equation of third order is constructed to determine position vector of an arbitrary spacelike general helix. In terms of solution, we determine the parametric representation of the general helices from the intrinsic equations. Moreover, we give some examples to illustrate how to find the position vectors of a...

Source: http://arxiv.org/abs/0908.0041v1

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102

Sep 21, 2013
09/13

by
Ahmad T Ali

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Salkowski \cite{salkow}, one century ago, introduced a family of curves with constant curvature but non-constant torsion (Salkowski curves) and a family of curves with constant torsion but non-constant curvature (anti-Salkowski curves) in Euclidean 3-space $\e^3$. In this paper, we adapt definition of such curves to time-like curves in Minkowski 3-space $\e_1^3$. Thereafter, we introduce an explicit parametrization of a time-like Salkowski curves and a time-like Anti-Salkowski curves in...

Source: http://arxiv.org/abs/0905.1404v1

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Sep 19, 2013
09/13

by
Ahmad T Ali

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In this paper, we define a new special curve in Euclidean 3-space which we call {\it $k-$slant helix} and introduce some characterizations for this curve. This notation is generalization of a general helix and slant helix. Furthermore, we have given some necessary and sufficient conditions for the $k-$slant helix.

Source: http://arxiv.org/abs/0909.2390v1

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2.0

Jun 29, 2018
06/18

by
Ahmad T Ali

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This article explores the Conformal Ricci Collineations (CRCs) for the plane-symmetric static spacetime. The non-linear coupled CRC equations are solved to get the general form of conformal Ricci symmetries. In the non-degenerate case, it turns out that the dimension of the Lie algebra of CRCs is finite. In the case were the Ricci tensor is degenerate, it found that the algebra of CRCs for the plane-symmetric static spacetime is mostly, but not always, infinite dimensional. In one case of...

Topics: General Physics, Physics

Source: http://arxiv.org/abs/1606.04114

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2.0

Jun 28, 2018
06/18

by
Ahmad T Ali; Anil Kumar Yadav; Abdulah K Alzahrani

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We investigate some new similarity inhomogeneous solutions of anisotropic dark energy and perfect fluid in Bianchi type-I space-time. Three different equation of state parameters along the spatial directions are introduced to quantify the deviation of pressure from isotropy. We consider the case when the dark energy is minimally coupled to the perfect fluid as well as direct interaction with it. The Lie symmetry generators that leave the equation invariant are identified and we generate an...

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1512.04874

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3.0

Jun 28, 2018
06/18

by
Ahmad T Ali; Suhail Khan; Azeb Alghanemi

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In this paper Bianchi type I spacetimes are completely classified by their homothetic vectors in the context of Lyra geometry. The non-linear coupled Lyra homothetic equations are obtained and solved completely for different cases. In some cases, Bianchi type I spacetimes admit proper Lyra homothetic vectors (LHVs) for special choices of the metric functions, while there exist other cases where the spacetime under consideration admits only Lyra Killing vectors (LKVs). In all the possible cases...

Topics: General Physics, Physics

Source: http://arxiv.org/abs/1512.04427

In this work, we introduce some special Smarandache curves in the Euclidean space. We study Frenet-Serret invariants of a special case. Besides, we illustrate examples of our main results.

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Nov 1, 2015
11/15

by
Ahmad T. Ali

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In this paper, a family of ruled surfaces generated by some special curves using a Frenet frame of that curves in Euclidean 3-space is investigated. Some important results are obtained in the case of general helices as well as slant helices. Moreover, as an application, circular general helices, spherical general helices, Salkowski curves and circular slant helices, which illustrate the results, are provided and graphed.

Topics: Ruled surfaces, Frenet frame, General helices

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Sep 23, 2013
09/13

by
Ahmad T. Ali

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In this paper, we prove that the position vector of every space curve satisfies a vector differential equation of fourth order. Also, we determine the parametric representation of the position vector $\psi=\Big(\psi_1,\psi_2,\psi_3\Big)$ of general helices from the intrinsic equations $\kappa=\kappa(s)$ and $\tau=\tau(s)$ where $\kappa$ and $\tau$ are the curvature and torsion of the space curve $\psi$, respectively. Our result extends some knwown results. Moreover, we give four examples to...

Source: http://arxiv.org/abs/0904.0301v1

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3.0

Jun 30, 2018
06/18

by
Ahmad T. Ali; Anil Kumar Yadav; Farook Rahaman; Arkopriya Mallick

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In this paper we derive some new invariant solutions of Einstein-Maxwell's field equations for string fluid as source of matter in cylindrically symmetric space-time with Variable Magnetic Permeability. We also discuss the physical and eometrical properties of the models derived in the paper. The solutions, at least one of them, are interesting physically as they can explain the accelerating as well as singularity free Universe.

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1411.1417

In this paper, a family of ruled surfaces generated by some special curves using a Frenet frame of that curves in Euclidean 3-space is investigated. Some important results are obtained in the case of general helices as well as slant helices. Moreover, as an application, circular general helices, spherical general helices, Salkowski curves and circular slant helices, which illustrate the results, are provided and graphed.

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Sep 23, 2013
09/13

by
Ahmad T. Ali; Mehmet Onder

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In this paper, we define a rectifying spacelike curve in the Minkowski space-time $E_1^4$ as a curve whose position vector always lies in orthogonal complement $N^{\bot}$ of its principal normal vector field $N$. In particular, we study the rectifying spacelike curves in $E_1^4$ and characterize such curves in terms of their curvature functions.

Source: http://arxiv.org/abs/0904.0655v1

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Sep 22, 2013
09/13

by
Ahmad T. Ali; Melih Turgut

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In this paper, position vectors of a time-like curve with respect to standard frame of Minkowski space E$^3_1$ are studied in terms of Frenet equations. First, we prove that position vector of every time-like space curve in Minkowski space E$^3_1$ satisfies a vector differential equation of fourth order. The general solution of mentioned vector differential equation has not yet been found. By special cases, we determine the parametric representation of the general helices from the intrinsic...

Source: http://arxiv.org/abs/0906.3851v1

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Sep 22, 2013
09/13

by
Ahmad T. Ali; Rafael Lopez; Melih Turgut

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We introduce the notion of $k$-type slant helix in Minkowski space $\e_1^4$. For partially null and pseudo null curves in $\e_1^4$, we express some characterizations in terms of their curvature and torsion functions.

Source: http://arxiv.org/abs/1001.0458v1

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Sep 23, 2013
09/13

by
Ahmad T. Ali; Rafael López

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We consider a curve $\alpha=\alpha(s)$ in Minkowski 3-space $E_1^3$ and denote by $\{T,N,B}$ the Frenet frame of $\alpha$. We say that $\alpha$ is a slant helix if there exists a fixed direction $U$ of $E_1^3$ such that the function $$ is constant. In this work we give characterizations of slant helices in terms of the curvature and torsion of $\alpha$.

Source: http://arxiv.org/abs/0810.1464v1

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Sep 22, 2013
09/13

by
Ahmad T. Ali; Rafael López

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We consider a unit speed curve $\alpha$ in Euclidean four-dimensional space $E^4$ and denote the Frenet frame by $\{T,N,B_1,B_2\}$. We say that $\alpha$ is a slant helix if its principal normal vector $N$ makes a constant angle with a fixed direction $U$. In this work we give different characterizations of such curves in terms of their curvatures.

Source: http://arxiv.org/abs/0901.3324v1

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Sep 22, 2013
09/13

by
Ahmad T. Ali; Rafael López

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We consider a unit speed curve $\alpha$ in Euclidean $n$-dimensional space $E^n$ and denote the Frenet frame by $\{v_1,...,v_n\}$. We say that $\alpha$ is a cylindrical helix if its tangent vector $v_1$ makes a constant angle with a fixed direction $U$. In this work we give different characterizations of such curves in terms of their curvatures.

Source: http://arxiv.org/abs/0901.3325v1

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Sep 23, 2013
09/13

by
Ahmad T. Ali; Rafael López

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We consider a unit speed timelike curve $\alpha$ in Minkowski 4-space $E_1^4$ and denote the Frenet frame of $\alpha$ by $\{T,N,B_1,B_2\}$. We say that $\alpha$ is a generalized helix if one of the unit vector fields of the Frenet frame has constant scalar product with a fixed direction $U$ of $E_1^4$. In this work we study those helices where the function $$ is constant and we give different characterizations of such curves.

Source: http://arxiv.org/abs/0810.1460v1

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2.0

Jun 30, 2018
06/18

by
Anil Kumar Yadav; Ahmad T Ali

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In this paper, we derive some new invariant solutions of dark energy models in cylindrically symmetric space-time. To quantify the deviation of pressure from isotropy, we introduce three different time dependent skewness parameters along the spatial directions. The matter source consists of dark energy which is minimally interact with perfect fluid. We use symmetry analysis method for solving the non-linear partial differential equations (NLPDEs) which is more powerful than the classical...

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1405.3185

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2.0

Jun 29, 2018
06/18

by
Anil Kumar Yadav; Ahmad T. Ali; Saibal Ray; A. Mallick

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In this work, we perform the Lie symmetry analysis on the Einstein-Maxwell field equations in plane symmetric spacetime. Here Lie point symmetries and optimal system of one dimensional subalgebras are determined. The similarity reductions and exact solutions are obtained in connection to the evolution of universe. The present study deals with the electromagnetic energy of inhomogeneous universe where $F_{12}$ is the non-vanishing component of electromagnetic field tensor. To get a deterministic...

Topics: General Physics, Physics

Source: http://arxiv.org/abs/1611.08501

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Sep 23, 2013
09/13

by
Fathi M. Hamdoon; Ahmad T. Ali; Rafael Lopez

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In this paper we consider the equiform motion of a sphere in Euclidean space $\mathbf{E}^7$. We study and analyze the corresponding kinematic three dimensional surface under the hypothesis that its scalar curvature $\mathbf{K}$ is constant. Under this assumption, we prove that $|\mathbf{K}|

Source: http://arxiv.org/abs/0904.1457v1

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Sep 19, 2013
09/13

by
Mostafa F. El-Sabbagh; Ahmad T. Ali

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In this paper, we define a new family of curves and call it a {\it family of similar curves with variable transformation} or briefly {\it SA-curves}. Also we introduce some characterizations of this family and we give some theorems. This definition introduces a new classification of a space curve. Also, we use this definition to deduce the position vectors of plane curves, general helices and slant helices, as examples of a similar curves with variable transformation.

Source: http://arxiv.org/abs/0909.1108v1