Linear connections and geodesics on Fréchet manifolds (Q1916560)

This article generalizes the method of projection of linear connections on principal bundles, developed by K. M. Yegiazaryan, to the case of Fréchet manifolds: Let \(\gamma\) be a connection in a Fréchet principal bundle \((\mathcal{E},\pi,\mathcal{B},\mathcal{G})\) and \(\nabla\) be a \(\mathcal{G}\)-invariant linear connection on \(\mathcal{E}\), then \(\gamma\) and \(\nabla\) induce a linear connection on \(\mathcal{B}\). This method is applied to the case where \(\mathcal{E}\) is an open subset of a Fréchet vector space. As an example, a connection on the space of \(C^\infty\) conformal structures is defined and its curvature and its geodesics are calculated.