scholarly journals Conformal Vector Fields and the De-Rham Laplacian on a Riemannian Manifold

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 863
Author(s):  
Amira Ishan ◽  
Sharief Deshmukh ◽  
Gabriel-Eduard Vîlcu
Keyword(s):  
Differential Equation ◽  
Riemannian Manifold ◽  
Vector Field ◽  
Nontrivial Solution ◽  
Vector Fields ◽  
Dimensional Sphere ◽  
Conformal Vector Field ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
De Rham

We study the effect of a nontrivial conformal vector field on the geometry of compact Riemannian spaces. We find two new characterizations of the m-dimensional sphere Sm(c) of constant curvature c. The first characterization uses the well known de-Rham Laplace operator, while the second uses a nontrivial solution of the famous Fischer–Marsden differential equation.

scholarly journals Closed conformal vector fields on pseudo-Riemannian manifolds

2006 ◽  
Vol 2006 ◽  
pp. 1-8 ◽  
Author(s):  
D. A. Catalano
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Riemannian Manifolds ◽  
Vector Fields ◽  
Geometric Proof ◽  
Conformal Vector Field ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Local Coordinates

We give here a geometric proof of the existence of certain local coordinates on a pseudo-Riemannian manifold admitting a closed conformal vector field.

scholarly journals On the zeros of a conformal vector field

1974 ◽  
Vol 55 ◽  
pp. 1-3 ◽  
Author(s):  
David E. Blair
Keyword(s):  
Vector Field ◽  
Riemannian Manifolds ◽  
Vector Fields ◽  
Short Note ◽  
Killing Vector ◽  
Connected Components ◽  
Conformal Vector Field ◽  
Totally Geodesic Submanifolds ◽  
Conformal Vector ◽  
Conformal Vector Fields

In [1] S. Kobayashi showed that the connected components of the set of zeros of a Killing vector field on a Riemannian manifold (Mn,g) are totally geodesic submanifolds of (Mn,g) of even codimension including the case of isolated singular points. The purpose of this short note is to give a simple proof of the corresponding result for conformal vector fields on compact Riemannian manifolds. In particular we prove the following

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.

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 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.

A note on conformal vector fields on a Riemannian manifold

2014 ◽  
Vol 136 (1) ◽  
pp. 65-73 ◽  
Author(s):  
Sharief Deshmukh ◽  
Falleh Al-Solamy
Keyword(s):  
Riemannian Manifold ◽  
Vector Fields ◽  
Conformal Vector ◽  
Conformal Vector Fields

Conformal vector fields on almost co-Kähler manifolds

2021 ◽  
Vol 71 (6) ◽  
pp. 1545-1552
Author(s):  
Uday Chand De ◽  
Young Jin Suh ◽  
Sudhakar K. Chaubey
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Killing Vector Field ◽  
Kahler Manifolds ◽  
Conformal Vector Field ◽  
Kahler Manifold ◽  
Conformal Vector ◽  
Conformal Vector Fields

Abstract In this paper, we characterize almost co-Kähler manifolds with a conformal vector field. It is proven that if an almost co-Kähler manifold has a conformal vector field that is collinear with the Reeb vector field, then the manifold is a K-almost co-Kähler manifold. It is also shown that if a (κ, μ)-almost co-Kähler manifold admits a Killing vector field V, then either the manifold is K-almost co-Kähler or the vector field V is an infinitesimal strict contact transformation, provided that the (1,1) tensor h remains invariant under the Killing vector field.

Conformal Vector Fields and Ricci Soliton Structures on Natural Riemann Extensions

2021 ◽  
Vol 18 (2) ◽  
Author(s):  
Mohamed Tahar Kadaoui Abbassi ◽  
Noura Amri ◽  
Cornelia-Livia Bejan
Keyword(s):  
Vector Fields ◽  
Ricci Soliton ◽  
Conformal Vector ◽  
Conformal Vector Fields
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