Vanlı A.
American Mathematical Society, ss.1, Michigan, 2022
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Yayın Türü:
Bilirkişi Raporu / Uzmanlık Raporu
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Basım Tarihi:
2022
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Basıldığı Şehir:
Michigan
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Açık Arşiv Koleksiyonu:
AVESİS Açık Erişim Koleksiyonu
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Gazi Üniversitesi Adresli:
Evet
Özet
A smooth Riemannian manifold (Mn,g) is called an Einstein-type manifold if there exists a non-constant smooth function f:Mn→R that solves fRicg=∇2f+σg, where σ is a smooth function, Ricg is the Ricci tensor of g and ∇2f denotes the Hessian of f.
In this article, the authors prove that any K-contact manifold admitting an Einstein-type metric is isometric to a unit sphere. In addition, they show that any non-Sasakian (k,μ)-contact metric manifold M2n+1 for n>1 admitting an Einstein-type metric is locally isometric to the product of a Euclidean space Rn+1 and a sphere Sn of curvature 4, and M2n+1 is flat when n=1. Moreover, they prove that a similar conclusion also holds for a contact metric manifold admitting an Einstein-type metric with zero radial Weyl curvature and satisfying a commutativity condition.