scholarly journals $$ {\varphi }$$ (Ric)-vector fields on warped product manifolds and applications

2021 ◽  
Author(s):  
Uday Chand De ◽  
Sameh Shenawy ◽  
Bülent Ünal
Keyword(s):  
Warped Product ◽  
Vector Fields

Magnetic trajectories corresponding to Killing magnetic fields in a three-dimensional warped product

2020 ◽  
Vol 17 (14) ◽  
pp. 2050212
Author(s):  
Zafar Iqbal ◽  
Joydeep Sengupta ◽  
Subenoy Chakraborty
Keyword(s):  
Magnetic Fields ◽  
Warped Product ◽  
Vector Fields ◽  
Killing Vector ◽  
Three Dimensional ◽  
Charged Particles ◽  
Open Interval ◽  
Product Formula ◽  
Warping Function ◽  
Killing Vector Fields

The aim of this paper is to investigate Killing magnetic trajectories of varying electrically charged particles in a three-dimensional warped product [Formula: see text] with positive warping function [Formula: see text], where [Formula: see text] is an open interval in [Formula: see text] equipped with an induced semi-Euclidean metric on [Formula: see text]. First, Killing vector fields on [Formula: see text] are characterized and it is observed that lifts to [Formula: see text] of Killing vector fields tangent to [Formula: see text] are also Killing on [Formula: see text]. Now, any Killing vector field on [Formula: see text] corresponds to a Killing magnetic field on [Formula: see text]. Magnetic trajectories (also known as magnetic curves) of charged particles which move under the influence of Lorentz force generated by Killing magnetic fields on [Formula: see text] are obtained in both Riemannian and Lorentzian cases. Moreover, some examples are exhibited with pictures determining Killing magnetic trajectories in hyperbolic [Formula: see text]-space [Formula: see text] modeled by the Riemannian warped product [Formula: see text]. Furthermore, some examples of spacelike, timelike and lightlike Killing magnetic trajectories are given with their possible graphs in the Lorentzian warped product [Formula: see text].

scholarly journals Lightlike hypersurfaces in spaces with concircular fields

2021 ◽  
Author(s):  
Samuel Ssekajja
Keyword(s):  
Riemannian Manifolds ◽  
Warped Product ◽  
Vector Fields ◽  
Totally Geodesic ◽  
Special Cases ◽  
Lightlike Hypersurfaces

AbstractLightlike hypersurfaces in semi-Riemannian manifolds admitting concircular vector fields are investigated. We prove that such hypersurfaces are generally products of lightlike curves and warped product manifolds. In special cases, we show that these hypersurfaces are totally geodesic or totally screen geodesic provided such concircular fields belong to their normal or transversal bundles. A number of examples are furnished, where possible, to illustrate the main concepts.

scholarly journals Sequential warped products: Curvature and conformal vector fields

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4071-4083
Author(s):  
Uday De ◽  
Sameh Shenawy ◽  
Bülent Ünal
Keyword(s):  
Warped Product ◽  
Vector Fields ◽  
Killing Vector ◽  
Warped Products ◽  
Covariant Derivatives ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Different Types ◽  
New Type ◽  
Static Space

In this note, we introduce a new type of warped products called as sequential warped products to cover a wider variety of exact solutions to Einstein?s field equation. First, we study the geometry of sequential warped products and obtain covariant derivatives, curvature tensor, Ricci curvature and scalar curvature formulas. Then some important consequences of these formulas are also stated. We provide characterizations of geodesics and two different types of conformal vector fields, namely, Killing vector fields and concircular vector fields on sequential warped product manifolds. Finally, we consider the geometry of two classes of sequential warped product space-time models which are sequential generalized Robertson-Walker space-times and sequential standard static space-times.

scholarly journals Conformal Vector Fields on Doubly Warped Product Manifolds and Applications

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
H. K. El-Sayied ◽  
Sameh Shenawy ◽  
Noha Syied
Keyword(s):  
Warped Product ◽  
Vector Fields ◽  
Sufficient Conditions ◽  
Ricci Solitons ◽  
Ricci Collineations ◽  
Conformal Vector ◽  
Conformal Vector Fields

This article aimed to study and explore conformal vector fields on doubly warped product manifolds as well as on doubly warped spacetime. Then we derive sufficient conditions for matter and Ricci collineations on doubly warped product manifolds. A special attention is paid to concurrent vector fields. Finally, Ricci solitons on doubly warped product spacetime admitting conformal vector fields are considered.

scholarly journals 2-Killing vector fields on warped product manifolds

2015 ◽  
Vol 26 (09) ◽  
pp. 1550065 ◽  
Author(s):  
Sameh Shenawy ◽  
Bülent Ünal
Keyword(s):  
Vector Field ◽  
Product Space ◽  
Warped Product ◽  
Vector Fields ◽  
Killing Vector ◽  
Killing Vector Field ◽  
Product Manifold ◽  
Killing Vector Fields ◽  
Warped Product Manifold

This paper provides a study of 2-Killing vector fields on warped product manifolds as well as characterization of this structure on standard static and generalized Robertson–Walker space-times. Some conditions for a 2-Killing vector field on a warped product manifold to be parallel are obtained. Moreover, some results on the curvature of a warped product manifolds in terms of 2-Killing vector fields are derived. Finally, we apply our results to describe 2-Killing vector fields of some well-known warped product space-time models.

scholarly journals Solutions to the affine quasi-Einstein equation for homogeneous surfaces

2020 ◽  
Vol 20 (3) ◽  
pp. 413-432
Author(s):  
M. Brozos-Vázquez ◽  
E. García-Río ◽  
P. Gilkey ◽  
X. Valle-Regueiro
Keyword(s):  
Einstein Equation ◽  
Warped Product ◽  
Vector Fields ◽  
Einstein Metrics ◽  
Killing Vector ◽  
Einstein Manifolds ◽  
Killing Vector Fields ◽  
Organizational Framework ◽  
Yamabe Solitons

AbstractWe examine the space of solutions to the affine quasi–Einstein equation in the context of homogeneous surfaces. As these spaces can be used to create gradient Yamabe solitons, conformally Einstein metrics, and warped product Einstein manifolds using the modified Riemannian extension, we provide very explicit descriptions of these solution spaces. We use the dimension of the space of affine Killing vector fields to structure our discussion as this provides a convenient organizational framework.

Normal Forms and Bifurcation of Planar Vector Fields

1994 ◽  
Author(s):  
Shui-Nee Chow ◽  
Chengzhi Li ◽  
Duo Wang
Keyword(s):  
Vector Fields ◽  
Normal Forms ◽  
Planar Vector Fields ◽  
Planar Vector

Parallel Computation of Complex Antennas around the Coated Object Using Iterative Vector Fields Technique

2014 ◽  
Vol E97.C (7) ◽  
pp. 661-669
Author(s):  
Ying YAN ◽  
Xunwang ZHAO ◽  
Yu ZHANG ◽  
Changhong LIANG ◽  
Zhewang MA
Keyword(s):  
Parallel Computation ◽  
Vector Fields
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