EGFLOW

Extrinsic Geometric Flows on Foliated Manifolds

Coordinatore	UNIVERSITY OF HAIFA    more  Organization address address: "Mount Carmel, Abba Khoushi Blvd." city: HAIFA postcode: 31905 contact info Titolo: Ms. Nome: Suzan Cognome: Aminpour Email: send email Telefono: +972 4 8240549 Fax: +972 4 8288035
Nazionalità Coordinatore	Israel [IL]
Totale costo	45˙000 €
EC contributo	45˙000 €
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-2010-RG
Funding Scheme	MC-ERG
Anno di inizio	2011
Periodo (anno-mese-giorno)	2011-06-01   -   2014-05-31

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	UNIVERSITY OF HAIFA  Organization address address: "Mount Carmel, Abba Khoushi Blvd." city: HAIFA postcode: 31905 contact info Titolo: Ms. Nome: Suzan Cognome: Aminpour Email: send email Telefono: +972 4 8240549 Fax: +972 4 8288035	IL (HAIFA)	coordinator	45˙000.00

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 Obiettivo del progetto (Objective)

'The project investigates the extrinsic geometry of foliations (expressed by the 2nd fundamental form of leaves) using the approach of the geometric flows.

We propose to study not just a single foliated manifold (M, F, g), but rather – assuming a suitable local existence theory – a foliation with a one-parameter family of F-truncated metrics gt parametrized by a ‘time’ t.

The research objectives are to develop Extrinsic Geometric Flow (EGF) on foliated manifolds recently introduced by the applicant (commonly with P. Walczak, arXiv:1003.1607v1) for codimension-one foliations as a new research tool for studying the extrinsic geometry of foliations. We shall also use the methods of geometric analysis and PDE’s, theory of Riemannian submanifolds, integral formulae for foliations, topology and dynamics of foliations, and computer simulations.

The (hoped for) results concern

(i) Development of EGF for a foliation of codimension-1 and of arbitrary codimension: existence and uniqueness theorems, converging as , behavior of curvature, singularities, extrinsic geometric solitons (for totally umbilical metrics, foliated surfaces and 3-manifolds), F-truncated variations of related total quantities and geometry of stable critical metrics etc;

(ii) Applications of EGF to solutions of various problems (by Gluck-Ziller, Walczak, Toponogov etc) concerning the extrinsic geometry of foliations: minimizing functions like volume and energy defined for plane fields on Riemannian manifolds, the extrinsic Ricci and Newton transformation flows, foliated Riemannian submanifolds, combining integral formulae for real and complex foliations with the approach of EGF etc.

The topic belongs to differential geometry and topology, subjects of pure mathematics.'