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Integral formulae and extrinsic geometry of foliations

Ziel

The project concerns investigations of the extrinsic geometry (expressed by the 2nd fundamental form of leaves) and its relations with mixed curvature, topology and dynamics of foliations on compact (or of finite volume) manifolds. The research objectives are to go deeply in studying foliations using the methods of Riemannian geometry, theory of submanifolds, topology and dynamics, computer simulations. Among the (hoped for) results are new integral formulae for foliations on Riemannian manifolds, connectedness properties of (k, ε)-saddle (saddle, totally geodesic) foliations, and applications of them to the following problems: – Walczak problem: to recover a metric on a foliated manifold by higher mean curvatures of a foliation or its orthogonal distribution; – Gluck-Ziller problem: minimizing certain functions like volume and energy defined for plane fields on Riemannian manifolds, considered as maps into the (co)tangent Grassmann bundles equipped with Cheeger-Gromoll type metrics; – Toponogov problem: to generalize Ferus’s theorem for the case of foliations with non-negative (positive) mixed curvature. The topic belongs to differential geometry and topology, subjects of pure mathematics.

Aufforderung zur Vorschlagseinreichung

FP7-PEOPLE-2007-2-1-IEF
Andere Projekte für diesen Aufruf anzeigen

Koordinator

UNIWERSYTET LODZKI
EU-Beitrag
€ 161 533,53
Adresse
UL PREZYDENTA GABRIELA NARUTOWICZA 68
90-136 LODZ
Polen

Auf der Karte ansehen

Region
Makroregion centralny Łódzkie Miasto Łódź
Aktivitätstyp
Higher or Secondary Education Establishments
Kontakt Verwaltung
Pawel Walczak (Prof.)
Links
Gesamtkosten
Keine Daten