In this paper, firstly we define the notions of T-magnetic, N-magnetic and B-magnetic pseudo null curves in Minkowski 3-space, obtain the magnetic vector field V when the pseudo null curve is a T-magnetic, N-magnetic and B-magnetic trajectory of V and give an example for these magnetic curves. After, we define the notions of ξ-magnetic, Nmagnetic and W-magnetic null curves in Minkowski 3-space. Also, by obtaining the Lorentz force according to the Cartan frame of these curves, we investigate the existence of a magnetic vector field V of a curve α to be α is a ξ-magnetic, N-magnetic or W-magnetic null trajectory of V .

In this paper, we define the notions of T-magnetic, N1-magnetic, N2-magnetic curves according to Bishop frame and ξ1-magnetic, ξ2-magnetic, B-magnetic curves according to type-2 Bishop frame in Euclidean 3-space. Also, we obtain the magnetic vector field V when the curve is T-magnetic, N1-magnetic, N2-magnetic trajectory of V according to Bishop frame and ξ1-magnetic, ξ2-magnetic, B-magnetic trajectory of V according to type-2 Bishop frame. Finally, we give an example for magnetic curves according to Bishop frame and type-2 Bishop frame.

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Bu çalışmada, ilk olarak 4-boyutlu Öklidyen uzayında bir Monge hiperyüzeyinin ortalama ve Gaussian eğriliklerini verdik. Ardından, farklı yoğunluklara sahip uzayında Monge hiperyüzeylerini çalıştık. Bu bağlamda, ve hepsi aynı anda sıfır olmayan sabitler olmak üzere, (lineer yoğunluk) ve yoğunluklu uzayında ağırlıklı minimal ve ağırlıklı flat Monge hiperyüzeylerini ve sabitlerinin farklı seçimleri yardımıyla elde ettik. Anahtar Kelimeler:Yoğunluklu manifold, ağırlıklı ortalama eğrilik, ağırlıklı gaussian eğriliği, monge yüzeyleri.

Abstract:In this paper, we construct the twisted surfaces according to the supporting plane and type of rotations in pseudo-Galilean space G 1 3 . Also, we find the Gaussian curvatures and mean curvatures of the different types of these twisted surfaces and draw some figures for these twisted surfaces.

In the present paper, firstly we express the relation between the semi-symmetric metric con-nection∇ and the torsion-free connection ∇ and obtain the relation between the curvature tensorsR of∇ and R of ∇. After, we obtain these relations for∇ and the dual connection ∇ *. Also, we give the relations between the curvature tensorR of semi-symmetric metric connection∇ and the curvature tensors R and R * of the connections ∇ and ∇ * on Sasakian statistical manifolds, respectively. We obtain the relations between the Ricci tensor (and scalar curvature) of semi-symmetric metric connection∇ and the Ricci tensors (and scalar curvatures) of the connections ∇ and ∇ *. Finally, we construct an example of a 3-dimensional Sasakian manifold with statistical structure admitting the semi-symmetric metric connection in order to verify our results.

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In this paper we obtain a condition for the tangent bundle .TM; Q J ; Q g/ to be locally decomposable Golden Riemannian tangent bundle, where Q J is the Golden structure on TM and Q g is the Cheeger-Gromoll metric.