On the holonomization of semiholonomic jets
Bull. Korean Math. Soc. 2015 Vol. 52, No. 4, 1365-1373
Printed July 31, 2015
W{\l}odzimierz M. Mikulski
Jagiellonian University
Abstract : We find all $\F\M_m$-natural operators $A$ transforming torsion free classical linear connections $\nabla$ on $m$-manifolds $M$ into base preserving fibred maps $A(\nabla):\overline J^rY\to J^rY$ for $\F\M_m$-objects $Y$ with bases $M$, where $\overline J^r$, $J^r$ are the semiholonomic and holonomic jet functors of order $r$ on the category $\F\M_m$ 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
MSC numbers : 58A05, 58A20, 58A32
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