[Turkmath:6773] TUBITAK Feza Gursey Enstitusu, January 19 (Tuesday), 2010 - 14:00, Graham S. Hall (Institute of Mathematics, University of Aberdeen), Projective Structure in Differential Geometry and Physics

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TUBITAK Feza Gursey Enstitusu
January 19 (Tuesday), 2010 - 14:00
*Graham S. Hall* (Institute of Mathematics, University of Aberdeen)
*Projective Structure in Differential Geometry and Physics*

*Abstract:* This talk asks the following question. Suppose M is a 
manifold and g and g' are Lorentz metrics on M with Levi-Civita 
connections D and D', respectively. Suppose that the unparametrised 
geodesic paths on M for D and D' are the same. How are g and g' (and D 
and D') related? [By an "unparametrised" geodesic path is meant the 
actual geodesic path in M, ignoring the parameter of the path.]

This talk is of interest as a mathematical question in pure differential 
geometry and also in general relativity theory because of the 
Newton-Einstein principle of equivalence. The idea is to show that for 
many situations, D and D' are tightly related as also are g and g' and 
in many cases, the "best possible" result, D=D', follows.

The plan of the talk is to discuss, firstly, some general techniques for 
approaching this problem and second, to introduce holonomy theory as a 
convenient and powerful tool for solving it. In many cases holonomy 
theory can resolve the problem for the relationship between g and g' if 
D=D'.
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