FHOGS · Flow and Harmonicity of Geometric Structures
7РП — „Хора“ (Действия „Мария Кюри“)
- Период
- 2008-10-01 → 2010-09-30
- Финансиране от ЕС
- 154 345 €
- Участници
- 1
- Схема
- MC-IEF
Линиите свързват координатора с партньорите.
Накратко на български
Хармоничните сечения на геометрични структури се анализират чрез математически потоци, като например при повърхности в Кяхлерви многообразия. Работата помага за по-доброто разбиране на вариационните принципи и разграничаването на сложни геометрични обекти.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Цел на проекта
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.
Оригинален текст от CORDIS (на английски).
Участници
- UNIVERSITE DE BREST · BRESTКоординаторФранция
Връзки
Данни: CORDIS, © Европейски съюз