ON THE HOLONOMIZATION OF SEMIHOLONOMIC JETS

@article{Mikulski2015ONTH,
  title={ON THE HOLONOMIZATION OF SEMIHOLONOMIC JETS},
  author={Włodzimierz M. Mikulski},
  journal={Bulletin of The Korean Mathematical Society},
  year={2015},
  volume={52},
  pages={1365-1373}
}
  • W. Mikulski
  • Published 31 July 2015
  • Mathematics
  • Bulletin of The Korean Mathematical Society
Abstract. We find all FM m -natural operators Atransforming torsionfree classical linear connections ∇on m-manifolds M into base preservingfibred maps A(∇) : J r Y → J r Y for FM m -objects Y with bases M,where J r , J r are the semiholonomic and holonomic jet functors of orderr on the category FM m of fibred manifolds with m-dimensional basesand their fibred maps with embeddings as base maps. 0. IntroductionAll manifolds considered in the paper are assumed to be finite dimensional,without… 
On the symmetrization of jets on vector bundles
We solve the existence problems of holonomic prolongation of general linear connections and the symmetrization of semiholonomic jets on vector bundles.

References

SHOWING 1-10 OF 12 REFERENCES
Introduction to the theory of semi-holonomic jets
To Ivan Koll a r on the occasion of his 60th birthday. The usual jets were introduced by C. Ehresmann as a fundamental tool in Diierential Geometry. They permit to globalize the theory of diierential
On symmetrization of jets
Let F = F(A,H,t) and $${F^1} = {F^{({A^1},{H^1},{t^1})}}$$ be fiber product preserving bundle functors on the category FMm of fibred manifolds Y with m-dimensional bases and fibred maps covering
Higher-Order Differential Equations Represented by Connections on Prolongations of a Fibered Manifold
The main goal of the present work is a generalization of the ideas, constructions and results from the first and second-order situation, studied in [63], [64] to that of an arbitrary finite-order
Natural operations in differential geometry
I. Manifolds and Lie Groups.- II. Differential Forms.- III. Bundles and Connections.- IV. Jets and Natural Bundles.- V. Finite Order Theorems.- VI. Methods for Finding Natural Operators.- VII.
Weil bundles as generalized jet spaces
On the fiber product preserving bundle functors
Natural maps depending on reductions of frame bundles
We clarify how the natural transformations of fiber product preserving bundle functors on the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local
The Geometry of Jet Bundles
Introduction 1. Bundles 2. Linear bundles 3. Linear operations on general bundles 4. First-order jet bundles 5. Second-order jet bundles 6. Higher-order jet bundles 7. Infinite jet bundles
...
1
2
...