Browsing by Author "Shenawy, S."

Now showing 1 - 6 of 6

Open Access
2-Killing vector fields on warped product manifolds
(World Scientific Publishing, 2015) Shenawy, S.; Ünal, B.
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. © 2015 World Scientific Publishing Company.
Open Access
Concircular curvature on warped product manifolds and applications
(Springer, 2020-09) De, U. C.; Shenawy, S.; Ünal, Bülent
This study aims mainly at investigating the effects of concircular flatness and concircular symmetry of a warped product manifold on its fiber and base manifolds. Concircularly flat and concircularly symmetric warped product manifolds are investigated. The divergence-free concircular curvature tensor on warped product manifolds is considered. Finally, we apply some of these results to generalized Robertson–Walker and standard static space-times.
Open Access
Ricci solitons on singly warped product manifolds and applications
(Elsevier BV * North-Holland, 2021-08) De, U. C.; Mantica, C. A.; Shenawy, S.; Ünal, Bülent
The purpose of this article is to study implications of a Ricci soliton warped product manifold to its base and fiber manifolds. First, it is proved that if a warped product manifold is Ricci soliton then its factors are Ricci soliton. Then we study Ricci soliton on warped product manifolds admitting either a conformal vector field or a concurrent vector field. Finally, we study Ricci soliton on some warped product space-times.
Open Access
Sequential warped products: curvature and conformal vector fields
(University of Nis, 2019) Chand De, Uday; Shenawy, S.; Ünal, Bülent
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.
Open Access
The W2-curvature tensor on warped product manifolds and applications
(World Scientific Publishing, 2016) Shenawy, S.; Ünal, B.
The purpose of this paper is to study the W2-curvature tensor on (singly) warped product manifolds as well as on generalized Robertson-Walker and standard static space-times. Some different expressions of the W2-curvature tensor on a warped product manifold in terms of its relation with W2-curvature tensor on the base and fiber manifolds are obtained. Furthermore, we investigate W2-curvature flat warped product manifolds. Many interesting results describing the geometry of the base and fiber manifolds of a W2-curvature flat warped product manifold are derived. Finally, we study the W2-curvature tensor on generalized Robertson-Walker and standard static space-times; we explore the geometry of the fiber of these warped product space-time models that are W2-curvature flat. © 2016 World Scientific Publishing Company.
Open Access
φ (Ric)-vector fields on warped product manifolds and applications
(Springer, 2021-11) Chand De, U.; Shenawy, S.; Ünal, Bülent
Sufficient and necessary conditions are provided on warped product manifolds and their base and fiber manifolds for a vector field φj to be a φ(Ric)-vector field , that is, ∇iφj=μRij where Rij is the Ricci tensor of M and μ is a scalar. Two warped product space-times admitting φ(Ric)-vector fields are considered. Lorentzian quasi-Einstein manifolds admitting a time-like φ(Ric)-vector field are shown to be either Ricci simple or a perfect fluid GRW space-time. The generators of a Lorentzian generalized quasi-Einstein manifold admitting a time-like φ(Ric)-vector field are eigenvectors of the Ricci tensor with zero eigenvalue.