scholarly journals A classification of conformal vector fields on the tangent bundle

2020 ◽  
Vol 72 (5) ◽  
Author(s):  
Zohre Raei ◽  
Dariush Latifi
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Conformal Transformations ◽  
Conformal Vector ◽  
Conformal Vector Fields

UDC 514.7 Let ( M , g ) be a Riemannian manifold and T M be its tangent bundle equipped with a Riemannian (or pseudo-Riemannian) lift metric derived from g .  We give a classification of infinitesimal fibre-preserving conformal transformations on the tangent bundle.

Classification of proper non-static cylindrically symmetric perfect fluid space-times via conformal vector fields in f(R) gravity

2020 ◽  
Vol 17 (10) ◽  
pp. 2050147 ◽  
Author(s):  
Fiaz Hussain ◽  
Ghulam Shabbir ◽  
Shabeela Malik ◽  
Muhammad Ramzan ◽  
A. H. Kara
Keyword(s):  
Perfect Fluid ◽  
Vector Fields ◽  
Direct Integration ◽  
Cylindrically Symmetric ◽  
Conformal Vector ◽  
Conformal Vector Fields

In this paper, we classify proper non-static cylindrically symmetric (CS) perfect fluid space-times via conformal vector fields (CVFs) in the [Formula: see text] gravity. In order to classify the space-times, we use the algebraic and direct integration approaches. In the process of classification, there exist 23 cases for which the considered space-times become proper non-static. By studying each case in detail, we find that the conformal vector fields are of dimensions two, three and fifteen in the [Formula: see text] gravity.

A note on classification of teleparallel conformal symmetries in non-static plane symmetric space-times in the teleparallel theory of gravitation using diagonal tetrads

2016 ◽  
Vol 13 (04) ◽  
pp. 1650046 ◽  
Author(s):  
Ghulam Shabbir ◽  
Alamgeer Khan ◽  
M. Amer Qureshi ◽  
A. H. Kara
Keyword(s):  
Symmetric Space ◽  
Vector Fields ◽  
Integration Technique ◽  
Plane Symmetric ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Teleparallel Theory ◽  
Theory Of Gravitation ◽  
Static Plane

In this paper, we explore teleparallel conformal vector fields in non-static plane symmetric space-times in the teleparallel theory of gravitation using the direct integration technique and diagonal tetrads. This study will also cover the static plane symmetric space-times as well. In the teleparallel theory curvature of the non-static plane symmetric space-times is zero and the presence of torsion allows more symmetries. In this study after solving the integrabilty conditions it turns out that the dimension of teleparallel conformal vector fields are 5, 6, 7 or 8.

scholarly journals Tangent bundle geometry from dynamics: Application to the Kepler problem

2017 ◽  
Vol 14 (03) ◽  
pp. 1750047 ◽  
Author(s):  
J. F. Cariñena ◽  
J. Clemente-Gallardo ◽  
J. A. Jover-Galtier ◽  
G. Marmo
Keyword(s):  
Vector Field ◽  
Harmonic Oscillator ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Kepler Problem ◽  
Second Order ◽  
Affine Spaces ◽  
Conformal Vector ◽  
Conformal Vector Fields

In this paper, we consider a manifold with a dynamical vector field and enquire about the possible tangent bundle structures which would turn the starting vector field into a second-order one. The analysis is restricted to manifolds which are diffeomorphic with affine spaces. In particular, we consider the problem in connection with conformal vector fields of second-order and apply the procedure to vector fields conformally related with the harmonic oscillator ([Formula: see text]-oscillators). We select one which covers the vector field describing the Kepler problem.

Classification of vacuum classes of plane fronted gravitational waves via proper conformal vector fields in f(R) gravity

2019 ◽  
Vol 16 (10) ◽  
pp. 1950151 ◽  
Author(s):  
Fiaz Hussain ◽  
Ghulam Shabbir ◽  
Muhammad Ramzan ◽  
Shabeela Malik
Keyword(s):  
Gravitational Waves ◽  
Vector Fields ◽  
Homothetic Vector ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Integration Techniques ◽  
Pp Wave ◽  
Wave Space ◽  
Theory Of Gravity

In this paper, we have studied proper conformal vector fields of pp-wave space-times in the [Formula: see text] theory of gravity using algebraic and direct integration techniques. From this study, we found that a very special class of pp-waves known as plane fronted gravitational waves (GWs) is a solution in the [Formula: see text] theory of gravity. In order to find proper conformal vector fields, plane GWs are further classified in ten cases. Studying each case in detail it turns out that in two cases proper conformal vector fields exist while in the rest of eight cases, conformal vector fields become homothetic vector fields.

A note on classification of spatially homogeneous rotating space-times in f(R) theory of gravity according to their proper conformal vector fields

2019 ◽  
Vol 16 (07) ◽  
pp. 1950111 ◽  
Author(s):  
Ghulam Shabbir ◽  
Fiaz Hussain ◽  
Muhammad Ramzan ◽  
Ashfaque H. Bokhari
Keyword(s):  
Vector Fields ◽  
Space Time ◽  
Conformally Flat ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Spatially Homogeneous ◽  
Theory Of Gravity

In this paper, we present a study of proper conformal vector fields of spatially homogeneous rotating space-times in the [Formula: see text] theory of gravity. A total of six cases have been discussed in detail. It is found that the conformally non-flat spatially homogeneous rotating space-times do not admit proper conformal vector fields, while in a conformally flat case the space-time admits 15 independent conformal vector fields.

Classification of proper teleparallel conformal symmetry of spherically symmetric static spacetimes using diagonal tetrads

2020 ◽  
Vol 35 (28) ◽  
pp. 2050232
Author(s):  
Muhammad Amer Qureshi ◽  
Ghulam Shabbir ◽  
K. S. Mahomed ◽  
Taha Aziz
Keyword(s):  
Vector Fields ◽  
Conformal Symmetry ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Conformal Vector Field ◽  
Integration Technique ◽  
Killing Vector Fields ◽  
Conformal Vector ◽  
Conformal Vector Fields

We study proper teleparallel conformal vector fields in spherically symmetric static spacetimes. The main objective of this paper is to present the classification for the above-mentioned spacetimes. The problem has been examined by two methods: direct integration technique and diagonal tetrads. We show that the spherically symmetric static spacetimes do not admit proper teleparallel conformal vector field, so are actually the teleparallel killing vector fields.

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