Displaying similar documents to “Natural transformations of separated jets”

Natural affinors on ( J r , s , q ( . , ℝ 1 , 1 ) 0 ) *

Włodzimierz M. Mikulski (2001)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let r , s , q , m , n ∈ ℕ be such that s ≥ r ≤ q . Let Y be a fibered manifold with m -dimensional basis and n -dimensional fibers. All natural affinors on ( J r , s , q ( Y , ℝ 1 , 1 ) 0 ) * are classified. It is deduced that there is no natural generalized connection on ( J r , s , q ( Y , ℝ 1 , 1 ) 0 ) * . Similar problems with ( J r , s ( Y , ℝ ) 0 ) * instead of ( J r , s , q ( Y , ℝ 1 , 1 ) 0 ) * are solved.

Natural transformations of semi-holonomic 3-jets

Gabriela Vosmanská (1995)

Archivum Mathematicum

Similarity:

Let J ¯ 3 be the functor of semi-holonomic 3 -jets and J ¯ 3 , 2 be the functor of those semi-holonomic 3 -jets, which are holonomic in the second order. We deduce that the only natural transformations J ¯ 3 → J ¯ 3 are the identity and the contraction. Then we determine explicitely all natural transformations J ¯ 3 , 2 → J ¯ 3 , 2 , which form two 5 -parameter families.

Natural maps depending on reductions of frame bundles

Ivan Kolář (2011)

Annales Polonici Mathematici

Similarity:

We clarify how the natural transformations of fiber product preserving bundle functors on ℱ ℳ m can be constructed by using reductions of the rth order frame bundle of the base, ℱ ℳ m being the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps. The iteration of two general r-jet functors is discussed in detail.