Generalized Ricci-Recurrent Weyl Manifolds

Year 2024, Volume: 17 Issue: 2, 378 - 387, 27.10.2024

Zehra Hafızoğlu Gökdağ , Güler Arsan

https://doi.org/10.36890/iejg.1360673

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.

Keywords

Generalized Ricci-recurrent Weyl manifold, quasi-Einstein Weyl manifold, harmonic conformal curvature tensor, Einstein Weyl manifold, concircular curvature tensor

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