Abstract
The object of the present paper was to introduce the notion of hyper generalized φ-recurrent Sasakian manifold and quasi generalized φ-recurrent Sasakian manifold and study its various geometric properties. The existence of hyper generalized φ-recurrent Sasakian manifold and quasi generalized φ-recurrent Sasakian manifold is proved by giving a proper example.
Highlights
The notion of contact geometry has evolved from the mathematical formalism of classical mechanics [1]
The notion of local symmetry of a Riemannian manifold has been weakened by several authors in many ways to a different extent
In [19], Shaikh and Roy introduce a generalized class of recurrent manifolds called quasi generalized recurrent manifolds
Summary
The notion of contact geometry has evolved from the mathematical formalism of classical mechanics [1]. A Riemannian manifold is called generalized φ-recurrent if its curvature tensor R satisfies the condition φ2((∇W R)(X, Y )Z) = A(W )R(X, Y )Z + B(W )P(X, Y )Z,. If ρ = υ, (5) reduces to the notion of quasi-generalized Ricci-recurrent manifold introduced by Shaikh and Roy [19]. In [19], Shaikh and Roy introduce a generalized class of recurrent manifolds called quasi generalized recurrent manifolds. In the “Quasi generalized φrecurrent manifold” section, we introduce a generalized class of φ-recurrent manifold called quasi generalized φ-recurrent manifold and we study this property in Sasakian manifold and obtained some interesting results. The existence of quasi generalized φ-recurrent Sasakian manifold is ensured by a proper example in the last section
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