A General Background of Higher Order Geometry and Induced Objects on Subspaces
نویسندگان
چکیده
The higher order bundles defined by an affine bundle E and a vector pseudofield on E are investigated this paper. The acceleration bundles become nontrivial examples which motivate the above extension. Moreover, the main ideas of our construction can be used as well in other cases. Using affine bundles, a dual theory between Lagrangians and Hamiltonians (via Legendre transformations) is considered. A canonical way to induce a Hamiltonian on an affine subbundle is given, too. Mathematics Subject Classification: 14R25, 44A15, 70S05
منابع مشابه
On descent for coalgebras and type transformations
We find a criterion for a morphism of coalgebras over a Barr-exact category to be effective descent and determine (effective) descent morphisms for coalgebras over toposes in some cases. Also, we study some exactness properties of endofunctors of arbitrary categories in connection with natural transformations between them as well as those of functors that these transformations induce between co...
متن کاملKrylov Subspaces Associated with Higher-order Linear Dynamical Systems
A standard approach to model reduction of large-scale higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for model reduction of first-order systems. This paper presents some results about the structure of the block-Krylov subspaces induced by the matrices of such equivalent first-order formulations of hig...
متن کاملOn the k-nullity foliations in Finsler geometry
Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive...
متن کاملOn lifting of biadjoints and lax algebras
Given a pseudomonad $mathcal{T} $ on a $2$-category $mathfrak{B} $, if a right biadjoint $mathfrak{A}tomathfrak{B} $ has a lifting to the pseudoalgebras $mathfrak{A}tomathsf{Ps}textrm{-}mathcal{T}textrm{-}mathsf{Alg} $ then this lifting is also right biadjoint provided that $mathfrak{A} $ has codescent objects. In this paper, we give general results on lifting of biadjoints. As a consequence, ...
متن کاملParleda: a Library for Parallel Processing in Computational Geometry Applications
ParLeda is a software library that provides the basic primitives needed for parallel implementation of computational geometry applications. It can also be used in implementing a parallel application that uses geometric data structures. The parallel model that we use is based on a new heterogeneous parallel model named HBSP, which is based on BSP and is introduced here. ParLeda uses two main lib...
متن کامل