φ (Ric)-vector fields on warped product manifolds and applications

Sufficient and necessary conditions are provided on warped product manifolds and their base and fiber manifolds for a vector field φ j to be a φ Ric -vector field , that is, ∇ i φ j = μ R ij where R ij is the Ricci tensor of M and μ is a scalar. Two warped product space-times admitting φ Ric -vector...

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Bibliographic Details
Published in:Afrika mathematica 2021-11, Vol.32 (7-8), p.1709-1716
Main Authors: De, Uday Chand, Shenawy, Sameh, Ünal, Bülent
Format: Article
Language:English
Subjects:
Applications of Mathematics
Eigenvalues
Eigenvectors
Fields (mathematics)
History of Mathematical Sciences
Manifolds
Mathematical analysis
Mathematics
Mathematics and Statistics
Mathematics Education
Tensors
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Summary:Sufficient and necessary conditions are provided on warped product manifolds and their base and fiber manifolds for a vector field φ j to be a φ Ric -vector field , that is, ∇ i φ j = μ R ij where R ij 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.
ISSN:1012-9405
2190-7668
DOI:10.1007/s13370-021-00930-5