Generalized Recurrent and $\psi$-Recurrent Curvature on Mixed 3-Sasakian Manifolds

Articles in Press

Document Type : Original Scientific Paper

Authors

1 ‎Department of Mathematics‎, ‎University of Zanjan, ‎Zanjan‎, ‎I‎. ‎R‎. ‎Iran

2 ‎Department of Mathematics‎, University of Zanjan, ‎Zanjan‎, ‎I‎. ‎R‎. ‎Iran

3 ‎Department of Mathematics Education‎, ‎Farhangian University,‎ ‎Tehran‎, ‎I. R. ‎Iran

10.22052/mir.2026.257679.1543

Abstract

‎Considering the importance of mixed 3-Sasakian manifolds which admit Einstein metrics‎, ‎we introduce generalized mixed 3-$ \psi $-recurrent manifolds on mixed 3-Sasakian structures‎. ‎We prove that a non-flat generalized mixed 3-$\psi$-recurrent manifold is a generalized recurrent manifold with its horizontal vector fields‎. ‎Also‎, ‎we obtain a relation between associated 1-forms $\gamma_{i} $'s‎
‎and $\theta_{i} $'s for a generalized mixed 3-$ \psi$-recurrent manifold‎. ‎Moreover‎, ‎we give a necessary and sufficient condition for a mixed 3-Sasakian manifold to be a generalized mixed 3-$\psi$-recurrent‎. ‎Next‎, ‎we find the Riemannian curvature representation of a mixed 3-Sasakian manifold when that is a generalized mixed 3-$\psi$-recurrent‎.

Keywords

Main Subjects

References

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Mathematics Interdisciplinary Research

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Available Online from 17 June 2026

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