On 2-Killing and conformal vector fields on Riemannian manifolds

Fanaï, Hamid-Reza; Hessam, Hamed

doi:10.12988/imf.2017.46126

Cited by 3 publications

(1 citation statement)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Any Killing vector field is 2-Killing too, but not conversely. Nontrivial cases when a 2-Killing vector field is also Killing were given in [1,10]. We shall extend here some of those results.…”

Section: On 2-killing Vector Fieldssupporting

confidence: 58%

Killing and 2-Killing Vector Fields on Doubly Warped Products

Blaga,

Özgür

2023

Mathematics

View full text Add to dashboard Cite

We provide a condition for a 2-Killing vector field on a compact Riemannian manifold to be Killing and apply the result to doubly warped product manifolds. We establish a connection between the property of a vector field on a doubly warped product manifold and its components on the factor manifolds to be Killing or 2-Killing. We also prove that a Killing vector field on the doubly warped product gives rise to a Ricci soliton factor manifold if and only if it is an Einstein manifold. If a component of a Killing vector field on the doubly warped product is of a gradient type, then, under certain conditions, the corresponding factor manifold is isometric to the Euclidean space. Moreover, we provide necessary and sufficient conditions for a doubly warped product to reduce to a direct product. As applications, we characterize the 2-Killing vector fields on the doubly warped spacetimes, particularly on the standard static spacetime and on the generalized Robertson–Walker spacetime.

show abstract

Section: On 2-killing Vector Fieldssupporting

confidence: 58%