FHOGS

Flow and Harmonicity of Geometric Structures

 Coordinatore UNIVERSITE DE BRETAGNE OCCIDENTALE 

 Organization address address: RUE DES ARCHIVES 3
city: BREST CEDEX 3
postcode: 29238

contact info
Titolo: Ms.
Nome: Nathalie
Cognome: Queffelec
Email: send email
Telefono: -298016305
Fax: -298018346

 Nazionalità Coordinatore France [FR]
 Totale costo 154˙344 €
 EC contributo 154˙344 €
 Programma FP7-PEOPLE
Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
 Code Call FP7-PEOPLE-2007-2-1-IEF
 Funding Scheme MC-IEF
 Anno di inizio 2008
 Periodo (anno-mese-giorno) 2008-10-01   -   2010-09-30

 Partecipanti

# participant  country  role  EC contrib. [€] 
1    UNIVERSITE DE BRETAGNE OCCIDENTALE

 Organization address address: RUE DES ARCHIVES 3
city: BREST CEDEX 3
postcode: 29238

contact info
Titolo: Ms.
Nome: Nathalie
Cognome: Queffelec
Email: send email
Telefono: -298016305
Fax: -298018346

FR (BREST CEDEX 3) coordinator 0.00

Mappa


 Word cloud

Esplora la "nuvola delle parole (Word Cloud) per avere un'idea di massima del progetto.

sections    fibre    homogeneous    harmonic    maps    surfaces    objects    geometric    nearly    structure    section    flow    theme    theory    powerful    flows    variational    structures    leads   

 Obiettivo del progetto (Objective)

'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.'

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