Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE HOLONOMIZATION OF SEMIHOLONOMIC JETS

  • MIKULSKI, WLODZIMIERZ M. (INSTITUTE OF MATHEMATICS JAGIELLONIAN UNIVERSITY)
  • Received : 2014.10.25
  • Published : 2015.07.31
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Abstract

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

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References

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