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On a diagram in the theory of connections

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*Ercument Ortacgil*

**E-mail:** ortacgil@boun.edu.tr
**Abstract.** We study the correspondence between Christoffel and
Cartan symbols and construct a commutative diagram which relates the nonlinear
Janet sequences for the k$^{th}$ order Christoffel and Cartan symbols and
the nonlinear gauge sequence for the k$^{th}$ order coframe bundle.

**AMSclassification.** 53C05

**Keywords.** Christoffel and Cartan symbols, Janet sequence, gauge
sequence