Publication: Generalized Ricci-Recurrent Weyl Manifolds
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International Electronic Journal of Geometry, Person (Kazim ILARSLAN)
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Abstract
This present paper is concerned with the study of the generalized Ricci-recurrent Weyl manifolds. First, we obtain a sufficient condition for the generalized Ricci-recurrent Weyl manifold admitting harmonic conformal curvature tensor to be a quasi-Einstein Weyl manifold. Also, we give an example of a quasi-Einstein Weyl manifold. Then, we prove that a generalized Ricci-recurrent Weyl manifold satisfying the Codazzi type of Ricci tensor is an Einstein Weyl manifold if and only if its scalar curvature is a prolonged covariant constant. Moreover, we prove that a generalized Ricci-recurrent Weyl manifold with a generalized concircularly symmetric tensor is an Einstein-Weyl manifold whose scalar curvature is prolonged covariant constant.
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harmonic conformal curvature tensor, concircular curvature tensor, Special Riemannian manifolds (Einstein, Sasakian, etc.), Cebirsel ve Diferansiyel Geometri, Algebraic and Differential Geometry, generalized Ricci-recurrent Weyl manifold, Einstein-Weyl manifold, Generalized Ricci-recurrent Weyl manifold, quasi-Einstein Weyl manifold, harmonic conformal curvature tensor, Einstein Weyl manifold, concircular curvature tensor, Global Riemannian geometry, including pinching, quasi-Einstein Weyl manifold