Abstract
In this research, generalized and extended generalized $\phi $-recurrent Sasakian Finsler structures on horizontal and vertical tangent bundles and their various geometric properties are studied.
Highlights
Ruse defined a Riemannian space of the recurrent curvature for which the covariant derivation of the Riemannian curvature tensor R satisfies the relation: (∇sR)(p, q)r = A(s)R(p, q)r at all points for the non-zero 1-form A, in 1949 [13]
Generalized Ricci recurrent and generalized concircular recurrent manifolds are defined with the following relations, respectively: (∇sS)(p, q)r = A(s)S(p, q)r + B(s)g(p, q)r, (5)
In [1], the generalized φ -recurrent Sasakian manifold is defined with the following relation: φ 2((∇sR)(p, q)r) = A(s)R(p, q)r + B(s)g(p, q)r (9)
Summary
Ruse defined a Riemannian space of the recurrent curvature for which the covariant derivation of the Riemannian curvature tensor R satisfies the relation:. At all points for the non-zero 1-form A, in 1949 [13] In this relation, if A vanishes so the space is reduced to a locally symmetric manifold. Generalized Ricci recurrent and generalized concircular recurrent manifolds are defined with the following relations, respectively:. In [1], the generalized φ -recurrent Sasakian manifold is defined with the following relation:. F. Saglamer / On Generalized and Extended Generalized φ -recurrent Sasakian Finsler Structures for all vector fields p, q, r, s. Extended generalized φ -recurrency is one type of the extensions of φ -recurrency and discussed by Prakasha [11] and Jaiswal and Yadav [9] for Sasakian and trans-Sasakian manifolds. In [11], extended generalized φ -recurrent Sasakian manifold is defined in the following way:. These studies motivated us to discuss generalized φ recurrent and extended generalized φ -recurrent Sasakian Finsler structures
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