scholarly journals Prolongations of Connections to Tangential Fibre Bundles of Higher Order

1970 ◽  
Vol 40 ◽  
pp. 85-97 ◽  
Author(s):  
Akihiko Morimoto
Keyword(s):  
Tangent Bundle ◽  
Higher Order ◽  
Fibre Bundles ◽  
Affine Connections ◽  
Tangent Bundles

In the previous paper [3] we have studied the prolongations of G-structures to tangent bundles of higher order. The purpose of the present paper is to study the prolongations of connections to tangential fibre bundles of higher order, and to generalize the results due to S. Kobayashi [1] for the case of usual tangent bundle —— in fact, the arguments in [1] will be, in a sense, more or less simplified and clarified by using the notion of tangent bundles of higher order. In addition, as a consequence of our results, we shall obtain the prolongations of linear (affine) connections to tangent bundles of higher order.

scholarly journals Liftings of Tensor Fields and Connections to Tangent Bundles of Higher Order

1970 ◽  
Vol 40 ◽  
pp. 99-120 ◽  
Author(s):  
Akihiko Morimoto
Keyword(s):  
Arbitrary Order ◽  
Higher Order ◽  
Tensor Fields ◽  
Fibre Bundles ◽  
Affine Connections ◽  
Tangent Bundles

In the previous papers [1], [2] we have studied the prolongations of G-structures to tangent bundles of arbitrary order, and in [3] we have considered the prolongations of connections to the tangential fibre bundles of higher order. The purpose of the present paper is to study the liftings of tensor fields and affine connections to tangent bundles of higher order. In fact, most of results in [4], [5] will be generalized in a natural fashion and some of the formulas concerning vertical and complete lifts in [5] will be unified and generalized in our formulas concerning ‹Λ›-lifts (cf. §3).

scholarly journals Prolongations of G-Structures to Tangent Bundles of Higher Order

1970 ◽  
Vol 38 ◽  
pp. 153-179 ◽  
Author(s):  
Akihiko Morimoto
Keyword(s):  
Tangent Bundle ◽  
Higher Order ◽  
First Order ◽  
First Contact ◽  
Tangent Bundles ◽  
Derivatives Of ◽  
Special Case

In the previous paper [4] we have studied the prolongations of G-structures to tangent bundles. The purpose of the present paper is to generalize the previous prolongations and to look at them from a wide view as a special case by considering the tangent bundles of higher order. In fact, in some places, the arguments and calculations in [4] are more or less simplified. Since the usual tangent bundle T(M) of a manifold M considers only the first derivatives or first contact elements of M, the previous paper contains, in most parts, only the calculation of derivatives of first order.

scholarly journals Natural Paracontact Magnetic Trajectories on Unit Tangent Bundles

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 72
Author(s):  
Mohamed Tahar Kadaoui Abbassi ◽  
Noura Amri
Keyword(s):  
Gaussian Curvature ◽  
Tangent Bundle ◽  
Two Dimensional ◽  
Constant Gaussian Curvature ◽  
Metric Structures ◽  
Unit Tangent Bundle ◽  
Tangent Bundles ◽  
Full Classification ◽  
Kaluza Klein

In this paper, we study natural paracontact magnetic trajectories in the unit tangent bundle, i.e., those that are associated to g-natural paracontact metric structures. We characterize slant natural paracontact magnetic trajectories as those satisfying a certain conservation law. Restricting to two-dimensional base manifolds of constant Gaussian curvature and to Kaluza–Klein type metrics on their unit tangent bundles, we give a full classification of natural paracontact slant magnetic trajectories (and geodesics).

scholarly journals The extension of G-foliations to Tangent bundles of higher order

1975 ◽  
Vol 56 ◽  
pp. 29-44 ◽  
Author(s):  
Luis A. Cordero
Keyword(s):  
Infinite Sequence ◽  
Differentiable Manifold ◽  
Higher Order ◽  
Characteristic Classes ◽  
Tangent Bundles

In this paper we describe a canonical procedure for constructing the extension of a G-foliation on a differentiable manifold X to its tangent bundles of higher order and by applying the Bott-Haefliger’s construction of characteristic classes of G-foliations ([2], [3]) we obtain an infinite sequence of characteristic classes for those foliations (Theorem 4.8).

scholarly journals A Note on Tangent Bundles

1967 ◽  
Vol 29 ◽  
pp. 259-267 ◽  
Author(s):  
Kenichi Shiraiwa
Keyword(s):  
Homotopy Type ◽  
Tangent Bundle ◽  
Topological Structure ◽  
Differentiable Manifold ◽  
Differentiable Structure ◽  
Homotopy Types ◽  
Tangent Bundles

The tangent bundle of a differentiable manifold is an important invariant of a differentiable structure. It is determined neither by the topological structure nor by the homotopy type of a manifold. But in some cases tangent bundles depend only on the homotopy types of manifolds.

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