Objectif The use of variational principles to distinguish geometric objects is a fundamental theme of modern differential geometry: geodesics, minimal surfaces, Willmore surfaces, Einstein metrics, Yang-Mills fields. More generally, harmonic mappings have been introduced by Eells and Sampson and harmonic section theory applies this variational problem to sections of submersions. Especially interesting are bundles with homogeneous fibre G/H, where H is the reduced structure group corresponding to some additional geometric structure, since sections then parametrize H-structures. The theme of this project is to explore harmonic sections of geometric structures and adapt the powerful analytical technique of geometric flows. For example, the harmonic section equations are satisfied for nearly cosymplectic structures, if the characteristic field is parallel, or a hypersurface in a Kähler manifold. The general case has yet to be decided. One question is whether nearly Sasakian (or CR or warped product) structures are parametrized by harmonic sections. The 1-1 correspondence between f-structures (a generalisation of almost complex and contact structures) and sections of a homogeneous bundle leads to looking for f-structures for which the section is harmonic. The homogeneous fibre is neither irreducible nor symmetric, making the geometric analysis more intricate. The starting point of the theory of harmonic maps was the associated flow which inspired Hamilton's work on the Ricci flow, culminating with Perelman's proof of the Poincaré Conjecture. The variational nature of harmonic geometric structures naturally leads to considering the associated flow. This represents ground-breaking research as geometric flows have only been used for maps and curvatures. Viewing geometric structures as maps enables to extend this powerful tool to very geometrical objects. Champ scientifique natural sciencesmathematicspure mathematicsgeometry Mots‑clés Geometry Mathematical physics Programme(s) FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Thème(s) PEOPLE-2007-2-1.IEF - Marie Curie Action: "Intra-European Fellowships for Career Development" Appel à propositions FP7-PEOPLE-2007-2-1-IEF Voir d’autres projets de cet appel Régime de financement MC-IEF - Intra-European Fellowships (IEF) Coordinateur UNIVERSITE DE BRETAGNE OCCIDENTALE Contribution de l’UE € 154 344,74 Adresse RUE MATTHIEU GALLOU 3 29238 BREST France Voir sur la carte Région Bretagne Bretagne Finistère Type d’activité Higher or Secondary Education Establishments Contact administratif Nathalie Queffelec (Ms.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée
