New Methods in Finsler Geometry

A cardboard model for SOL geometry

speaker: Marc Troyanov (École Polytechnique Fédérale de Lausanne)

abstract: SOL is one of the classical eight Thurston's homogenous geometries (perhaps the most exotic one). A model of SOL is \(R^3\) with Riemannian metric \(ds^2 = dz^2 + exp(2z)dx^2 + exp(-2z)dy^2\) Supposeone wants to "see" the shape of large spheres in SOl (in the coordinate xyz-space), one should then be able to compute the distance between 2 points. But that is very complicate. On the other hand if one replace the Riemannian metric by a specific Finsler metric then one can explicitly compute distances and draw spheres. The Finsler metric is not the Riemannian metric of the original problem, but it is asymptotic in a precise sense and therefore the Finsler balls are very accurate models of the Riemannian balls. The Finsler metric is inspired by cardboards models in architecture and will be defined and discussed in the talk. The method can be generalized to other (Solvable groups) geometries.

timetable:
Mon 21 May, 10:40 - 11:30, Aula Dini
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