Objective
"The importance of ""gwistor space"" is being recognized today. The Researcher R. Albuquerque has discovered a natural G2 structure existing on the unit tangent sphere bundle of any given oriented Riemannian 4-manifold M. It was a major breakthrough in the theory of G2 manifolds and special structures.
That discovery has been appreciated by many great mathematicians. Firstly referred to as the ""G2 sphere of a 4-manifold"", the Researcher decided to call the bundle's total space the ""gwistor space"" of M. Also due to relations with genuine twistor theory.
Considering G2 geometry in general, it is known to be of great importance for its applications to String theory - but not only. There are few known examples satisfying several important equations of holonomy of metric-connections. On the other hand, mathematicians know that the geometry induced by the largest normed unit division algebra, the octonians, must comprise much more structure than it is understood today. E.g. the theory of associative calibrations, of special Riemannian submanifolds or relations with a proper gauge theory of G2-instantons are just in their beginning. Many aspects must be developed and that's where our project with gwistor space will give new answers.
Gwistor space is cocalibrated (the structure 3-form is coclosed) if and only if the base 4-manifold M is Einstein. This is undoubtedly a strong result in special Riemannian geometries. Giving new insight, on its own, to the long-sought theory of Einstein 4-manifolds.
Now, with this FP7 Project, the Researcher wishes to study a difficult problem, which arose from gwistors but is far more outstanding. Hidden aside of that structure was an exterior differential system (EDS) of Riemnanian manifolds in any dimension, the Griffiths system, and their Euler-Lagrange equations.
Many beautiful features of such EDS are now on a pre-published article. We may say it is of fundamental nature and importance for the great field which Riemannian geometry is."
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.
- natural sciences mathematics pure mathematics algebra
- natural sciences mathematics pure mathematics geometry
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Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
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.
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
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP7-PEOPLE-2012-IEF
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Funding Scheme
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.
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
10124 TORINO
Italy
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.