On golden semisymmetric metric $F$-connections

Gezer, Aydın; Karaman, Çağrı

doi:10.3906/mat-1510-77

Cited by 3 publications

(3 citation statements)

References 6 publications

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“…In [8], the product semi-symmetric non-metric connection was observed. Very interesting connections are also golden and metallic semi-symmetric connection that have been studied in a locally decomposable golden and metallic Riemannian manifold [1,2].…”

Section: Introductionmentioning

confidence: 99%

Notes on product semisymmetric connection in a locally decomposable Riemannian space

Maksimović¹,

Stankovic²

2021

Turk J Math

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The purpose of this paper is to investigate the product semi-symmetric connection in a locally decomposable Riemannian space. The curvature tensors of this connection were considered. Some properties of almost product structure, some properties of torsion tensor of product semi-symmetric connection and some relations between curvature tensors and almost product structure are given. Also, the paper checks a special case of such connection when its generator is a gradient vector.

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Section: Introductionmentioning

confidence: 99%

Notes on product semisymmetric connection in a locally decomposable Riemannian space

Maksimović¹,

Stankovic²

2021

Turk J Math

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“…Many authors have made interesting studies on golden and metallic manifolds. In one of them [4], they defined a semisymmetric metric F -connection on golden manifolds and made studies on it. A semisymmetric connection ∇ is a connection whose torsion tensor checks the equation S(U, V ) = w(V )U − w(U )V , where U , V are vector fields and w is a covector field.…”

Section: Introductionmentioning

confidence: 99%

On Holomorphic poly-Norden Manifolds

Karaman¹,

Topuz²

2020

Turk J Math

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In this paper, we investigated a new manifold with a poly-Norden structure, which is inspired by the positive root of the equation x 2 − mx − 1 = 0. We call this new manifold as holomorphic poly-Norden manifolds. We examine some properties of the Riemann curvature tensor and give an example of this manifold. Then, we define a different connection on this manifold which is named the semisymmetric metric poly F-connection and study some properties of the curvature and torsion tensor field according to this connection.

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“…One of them is a golden Riemann manifold (M; g; ') endowed with golden structure ' and Riemann metric tensor g. The golden structure ' created by Crasmareanu and Hretcanu is actually root of the equality ' 2 ' I = 0 [5]. In [2], the authors have de…ned golden semi-symmetric metric F connections on a locally decomposable golden Riemann manifold and examined torsion, projective curvature, conharmonic curvature and curvature tensors of this connection. Also, the golden ratio has many important generalizations.…”

Section: Introductionmentioning

confidence: 99%