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."
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
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Programme(s)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP7-PEOPLE-2010-RG
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Funding Scheme
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
31905 Haifa
Israel
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.