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Almost-geodesics on a Riemannian Hilbert manifold which are still almost geodesics in some s...

However, we do know that almost-geodesics always exist (see I. Ekeland: The Hopf-Rinow Theorem in infinite dimension. J. Diff. Geometry 13, 287-301 (1978)). … My question is related to a converse of this notion, which involves almost-geodesics instead of geodesics: under what conditions can we say that an almost-geodesic in $H$ is still an almost-geodesic in …
Manuel Norman's user avatar