Magnetic curves in tangent sphere bundles II

Natural Paracontact Magnetic Trajectories on Unit Tangent Bundles

“…In [1], the authors considered contact magnetic fields that are associated to the family of g-natural contact metric structures on the unit tangent bundle of a Riemannian manifold (cf. [2]) and studied the corresponding contact magnetic trajectories (we also refer to [3,4] for the Sasaki metric case).…”

Some Special Curves in the Unit Tangent Bundles of Surfaces

“…Hence, we write the Lie algebra of vector fields on as [11]. The induced Riemannian metric on from (1) is uniquely determined by (3) for every vector fields on and every tangent vector , where are constants. The conditions for to be positive are [6].…”

“…In studies on curves in the unit tangent sphere bundles, researchers generally consider the standard contact metric structure which is obtained by endowing the bundle with the induced Sasaki metric. For examples, in [1] Berndt et al studied the geodesics, in [2][3] Inoguchi and Munteanu investigated the magnetic curves, in [4] Hou and Sun considered the slant geodesics and in [5] Hathout et al discussed N-Legendre and N-slant curves of the unit tangent bundles with respect to this structure. However, some other contact metric structures can be defined on the unit tangent bundles.…”

Characteristic Jacobi Operator on Almost Cosymplectic 3-Manifolds

“…In our previous paper [22], trajectories of contact magnetic fields on cosymplectic manifolds are investigated. In addition, we studied trajectories of magnetic fields on E 2 derived from the left invariant contact metric structure in [32]. Here we propose the following problem: Problem 1.…”