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We present some interesting examples of dimension-3 open manifolds whose Riemannian geometry is far from being understood. This also gives us an opportunity to study several questions relating to the existence of "good" Riemannian metrics on those manifolds. Some of these examples are open sets of the 3-sphere.

Recording during the thematic meeting: «Spin geometry and analysis on manifolds » the October 07, 2014 at the Centre International de Rencontres Mathématiques (Marseille, France)

Filmmaker: Guillaume Hennenfent

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