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Rigidity of ( m , ρ ) ‐quasi Einstein manifolds
Author(s) -
Altay Demirbağ Sezgin,
Güler Sinem
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600186
Subject(s) - einstein , rigidity (electromagnetism) , mathematics , conformal map , einstein manifold , manifold (fluid mechanics) , pure mathematics , vector field , killing vector field , riemannian manifold , ricci flat manifold , pseudo riemannian manifold , product (mathematics) , mathematical analysis , mathematical physics , ricci curvature , physics , geometry , curvature , scalar curvature , quantum mechanics , mechanical engineering , engineering
This paper deals with the study on ( m , ρ ) ‐quasi Einstein manifolds. First, we give some characterizations of an ( m , ρ ) ‐quasi Einstein manifold admitting closed conformal or parallel vector field. Then, we obtain some rigidity conditions for this class of manifolds. We prove that an ( m , ρ ) ‐quasi Einstein manifold with a closed conformal vector field has a warped product structure of the form I × e q / 2M ∗ , where I is a real interval, ( M ∗ , g ∗ ) is an ( n − 1 ) ‐dimensional Riemannian manifold and q is a smooth function on I . Finally, a non‐trivial example of an ( m , ρ ) ‐quasi Einstein manifold verifying our results in terms of the potential function is presented.