Killing and 2-Killing Vector Fields on Doubly Warped Products

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...

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Bibliographic Details
Published inMathematics (Basel) Vol. 11; no. 24; p. 4983
Main Authors Blaga, Adara M., Özgür, Cihan
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.12.2023
Subjects
2-Killing vector field
Analysis
doubly warped product manifold
Euclidean geometry
Euclidean space
Fields (mathematics)
Fields, Algebraic
Ricci soliton
Riemann manifold
Riemann surfaces
Solitary waves
Spacetime
Vector spaces
Romania
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11244983