EDSRGFF

Exterior Differential Systems of Riemannian Geometry

Coordinatore	UNIVERSITA DEGLI STUDI DI TORINO    more  Organization address address: Via Giuseppe Verdi 8 city: TORINO postcode: 10124 contact info Titolo: Prof. Nome: Anna Maria Cognome: Fino Email: send email Telefono: 390117000000 Fax: 390117000000
Nazionalità Coordinatore	Italy [IT]
Totale costo	249˙242 €
EC contributo	249˙242 €
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-2012-IEF
Funding Scheme	MC-IEF
Anno di inizio	2013
Periodo (anno-mese-giorno)	2013-09-09   -   2015-09-08

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	UNIVERSITA DEGLI STUDI DI TORINO  Organization address address: Via Giuseppe Verdi 8 city: TORINO postcode: 10124 contact info Titolo: Prof. Nome: Anna Maria Cognome: Fino Email: send email Telefono: 390117000000 Fax: 390117000000	IT (TORINO)	coordinator	249˙242.80

Mappa

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 Obiettivo del progetto (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.'