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Integral formulae and extrinsic geometry of foliations

Objective

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.

Coordinator

UNIWERSYTET LODZKI

Address

Ul Prezydenta Gabriela Narutowicza 68
90 136 Lodz

Poland

Activity type

Higher or Secondary Education Establishments

EU Contribution

€ 161 533,53

Administrative Contact

Pawel Walczak (Prof.)

Project information

Grant agreement ID: 219696

Status

Closed project

  • Start date

    6 October 2008

  • End date

    5 October 2010

Funded under:

FP7-PEOPLE

  • Overall budget:

    € 161 533,53

  • EU contribution

    € 161 533,53

Coordinated by:

UNIWERSYTET LODZKI

Poland