ON THE HOLONOMIZATION OF SEMIHOLONOMIC JETS

Title & Authors
ON THE HOLONOMIZATION OF SEMIHOLONOMIC JETS
MIKULSKI, WLODZIMIERZ M.;

Abstract
We find all $\small{{\mathcal{F}}{\mathcal{M}}_m}$-natural operators A transforming torsion free classical linear connections $\small{{\nabla}}$ on m-manifolds M into base preserving fibred maps $\small{A({\nabla}):{\bar{J}}^rY{\rightarrow}J^rY}$ for $\small{{\mathcal{F}}{\mathcal{M}}_m}$-objects Y with bases M, where $\small{{\bar{J}}^r}$, $\small{J^r}$ are the semiholonomic and holonomic jet functors of order r on the category $\small{{\mathcal{F}}{\mathcal{M}}_m}$ of fibred manifolds with m-dimensional bases and their fibred maps with embeddings as base maps.
Keywords
fiber product preserving bundle functor;natural operator;classical linear connection;semiholonomic jet;holonomic jet;
Language
English
Cited by
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