Summary
Letl=(P, G, B, π) (resp.l′) be a principal bundle endowed with a connection ω (resp. ω′) and let (f, ϕ,h) be a morphism ofl intol′. Roughly speaking, ω and ω′ are (f, ϕ,h)-related it the morphism preserves the horizontal subspaces.
The main result is a criterion for such a relationship, under aG-B-isomorphism, given in terms of the corresponding local connection forms.
Since the connections on finite-dimensional trivial bundles correspond to ordinary differential systems, the above result leads to the usual transformations of (equivalent) systems and to the condition for the existence of a system with constant coefficient (Liapunoff).
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Based on a part of the author's doctoral thesis at the University of Athens.
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Vassiliou, E. (f, ϕ,h)-related connections and Liapunoff's theorem. Rend. Circ. Mat. Palermo 27, 337–346 (1978). https://doi.org/10.1007/BF02843891
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DOI: https://doi.org/10.1007/BF02843891