Transformations of linear connections. II
This paper is a continuation of the previous paper by the author [ibid. 13, 289-308 (1982; Zbl 0525.53044)] in which connections defined on Banachable fibre bundles were considered. Now, the author elucidates that paper with two applications. In the first, he views linear connections as systems of differential equations. Specializing this to the case of trivial bundles over \(S^ 1\), connections correspond to equations with periodic coefficients. Hence, applying the theory of Floquet, the author obtains a Floquet-type theorem for infinite-dimensional connections on such bundles. In the second example, he proves that the canonical connections of parallelizable manifolds are naturally derived from the canonical flat connection of appropriate trivial bundles.
linear connections on Banach vector bundles
scientific article; zbMATH DE number 4001019
scientific article