Einstein metrics are geodesically rigid

Host Institution:

La Trobe University

Title of Seminar:

Einstein metrics are geodesically rigid

Speaker's Name:

Prof Vladimir Matveev

Speaker's Institution:

University of Jena, Germany

Time and Date:

Friday 15 March, 3.00 PM (AEDT)

Seminar Abstract:

Certain astronomical observations allow us to determine only the UNPARAMETERISED geodesics of the space-time metric. This naturally leads to the following mathematical question explicitly asked by Weyl and Ehlers: how to determine a metric by its unparameterised geodesics? I will show that generally this problem cannot be solved uniquely (by showing examples of Lagrange and Levi-Civita of two different metrics with the same geodesics). The main mathematical theorem of my talk (I will give a rigorous proof) will be that 4D Einstein metrics of nonconstant curvature are geodesically rigid, in the sense that unparameterised geodesics determine such metrics uniquely. This is a result of joint work with V. Kiosak. I will also show some purely mathematical applications, one of which is a solution of a problem of S. Lie explicitly stated in 1882 (this part of the talk is based on a joint work R. Bryant and G. Manno).

Seminar Convenor:

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