Canonical Poisson–Nijenhuis structures on higher order tangent bundles

2014 ◽  
Vol 111 (1) ◽  
pp. 21-37
Author(s):  
P. M. Kouotchop Wamba
Keyword(s):  
Higher Order ◽  
Tangent Bundles ◽  
Order Tangent

Higher-order differential equations and higher-order lagrangian mechanics

1986 ◽  
Vol 99 (3) ◽  
pp. 565-587 ◽  
Author(s):  
M. Crampin ◽  
W. Sarlet ◽  
F. Cantrijn
Keyword(s):  
Order Differential Equation ◽  
Higher Order ◽  
Point Of View ◽  
Lagrangian Mechanics ◽  
First Order ◽  
The Subject ◽  
Tangent Bundles ◽  
Order Tangent ◽  
Higher Order Differential Equations ◽  
Number Of Authors

The study of higher-order mechanics, by various geometrical methods, in the framework of the theory of higher-order tangent bundles or jet spaces, has been undertaken by a number of authors recently: for example, Tulczyjew [16, 17], Rodrigues [14, 15] de León [8], Krupka and Musilova [11, and references therein]. In this article we wish to complement these studies by approaching the subject from a new point of view, one which we developed for second-order differential equation fields and first-order Lagrangian mechanics in [19]. In particular, our aim is to show that many of the results we obtained there may be extended to the higher-order case.

scholarly journals Higher Order Tangent Spaces and Influence Functions

2014 ◽  
Vol 29 (4) ◽  
pp. 679-686 ◽  
Author(s):  
Aad van der Vaart
Keyword(s):  
Higher Order ◽  
Influence Functions ◽  
Order Tangent

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).

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