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Full-Text Articles in Physical Sciences and Mathematics
Geodesics And Isocline Distributions In Tangent Bundles Of Nonflat Lorentzian-Heisenberg Spaces, Murat Altunbaş
Geodesics And Isocline Distributions In Tangent Bundles Of Nonflat Lorentzian-Heisenberg Spaces, Murat Altunbaş
Turkish Journal of Mathematics
Let $(H_{3},g_{1})$ and $(H_{3},g_{2})$ be the Lorentzian-Heisenberg spaces with nonflat metrics $g_{1}$ and $g_{2},\ $and $(TH_{3},g_{1}^{s}),\ (TH_{3},g_{2}^{s})$ be their tangent bundles with the Sasaki metric, respectively. In the present paper, we find nontotally geodesic distributions in tangent bundles by using lifts of contact forms from the base manifold $H_{3}.$We give examples for totally geodesic but not isocline distributions. We study the geodesics of tangent bundles by considering horizontal and natural lifts of geodesics of the base manifold $H_{3}$. We also investigate more general classes of geodesics which are not obtained from horizontal and natural lifts of geodesics.
Geodesics And Natural Complex Magnetic Trajectories On Tangent Bundles, Mohamed Tahar Kadaoui Abbassi, Noura Amri
Geodesics And Natural Complex Magnetic Trajectories On Tangent Bundles, Mohamed Tahar Kadaoui Abbassi, Noura Amri
Turkish Journal of Mathematics
In this paper, we investigate geodesics of the tangent bundle $TM$ of a Riemannian manifold $(M,g)$ endowed with an arbitrary pseudo-Riemannian $g$-natural metric of Kaluza-Klein type. Then considering a class of naturally defined almost complex structures on $TM$, constructed by V. Oproiu, we construct a class of magnetic fields and we characterize the corresponding magnetic curves on $TM$, when $(M,g)$ is a space form.
On The Geodesics Of Deformed Sasaki Metric, Nour Elhouda Djaa, Abderrahim Zagane
On The Geodesics Of Deformed Sasaki Metric, Nour Elhouda Djaa, Abderrahim Zagane
Turkish Journal of Mathematics
We define in this note a natural metric over the tangent bundle $TM$ by using a vertical deformation of Sasaki metric. First we present the geometric result concerning the Levi-Civita connection and all forms of Riemannian curvature tensors of this metric. Secondly, we study the geodesics on the tangent bundle $TM$ and unit tangent bundle $T_{1}M$. Finally, we characterize the geodesic curvatures on $T_{1}M$.
Geodesics Of Fiberwise Cigar Soliton Deformation Of The Sasaki Metric, Liana Lotarets
Geodesics Of Fiberwise Cigar Soliton Deformation Of The Sasaki Metric, Liana Lotarets
Turkish Journal of Mathematics
Ricci solitons arose in proof the Poincare conjecture by R. Hamilton and G. Perelman. The first example of a noncompact steady Ricci soliton on a plane was found by R. Hamilton. This two-dimensional manifold is conformally equivalent to the plane and it is called by R. Hamilton's cigar soliton. The cigar soliton metric can be considered as a fiber-wise conformal deformation of the Euclidean metric on a fiber of the tangent bundle. In the paper we propose a deformation of the classical Sasaki metric on the tangent bundle of an n-dimensional Riemannian manifold that induces the cigar soliton type metric …
On The Geometry Of Tangent Bundle Of A Hypersurface In $%%Tcimacro{\U{211d} }%%Beginexpansion\Mathbb{R}%Endexpansion^{N+1}$, Semra Yurttançikmaz
On The Geometry Of Tangent Bundle Of A Hypersurface In $%%Tcimacro{\U{211d} }%%Beginexpansion\Mathbb{R}%Endexpansion^{N+1}$, Semra Yurttançikmaz
Turkish Journal of Mathematics
In this paper, tangent bundle $TM$ of the hypersurface $M$ in $% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{n+1}$ has been studied. For hypersurface $M$ given by immersion $f:M\rightarrow %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{n+1},$ considering the fact that $F=df:TM\rightarrow %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{2n+2}$ is also immersion, $TM$ is treated as a submanifold of $% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{2n+2}.$ Firstly, an induced metric which is called rescaled induced metric has been defined on $TM,$ and the Levi-Civita connection has been calculated for this metric. Next, curvature tensors of tangent bundle $TM$ have been obtained. Finally, the orthonormal …
Geodesicity And Isoclinity Properties For The Tangent Bundle Of The Heisenberg Manifold With Sasaki Metric, Simona Luiza Druta, Paola Piu
Geodesicity And Isoclinity Properties For The Tangent Bundle Of The Heisenberg Manifold With Sasaki Metric, Simona Luiza Druta, Paola Piu
Turkish Journal of Mathematics
We prove that the horizontal and vertical distributions of the tangent bundle with the Sasaki metric are isocline, the distributions given by the kernels of the horizontal and vertical lifts of the contact form \omega on the Heisenberg manifold (H_3,g) to (TH_3,g^S) are not totally geodesic, and the distributions F^H=L(E_1^H,E_2^H) and F^V=L(E_1^V,E_2^V) are totally geodesic, but they are not isocline. We obtain that the horizontal and natural lifts of the curves from the Heisenberg manifold (H_3,g), are geodesics on the tangent bundle endowed with the Sasaki metric (TH_3,g^s), if and only if the curves considered on the base manifold are …