Tuesday, November 4, 2008

On the Arxiv:

Riemannian metrics having the same geodesics
with Berwald metrics

Abstract: In Theorem 1, we generalize the results of Szabo for Berwald metrics that are not necessary strictly convex: we show that for every Berwald metric F there always exists a Riemannian metric affine equivalent to F.
Further, we investigate geodesic equivalence of Berwald metrics. Theorem 2 gives a system of PDE that has a (nontrivial) solution if and only if the given essentially Berwald metric admits a Riemannian metric that is (nontrivially) geodesically equivalent to it. The system of PDE is linear and of Cauchy-Frobenius type, i.e., the derivatives of unknown functions are explicit expressions of the unknown functions.
As a corollary, we obtain that geodesic equivalence of an essentially Berwald and a Riemannian metrics is always affine equivalence provided both metrics are complete.

the link is http://arxiv.org/abs/0811.0031

Thursday, October 9, 2008

Workshop on
"Integral geometry and Finsler geometry".

It will take place in Fribourg (Switzerland) from January 21 to January 23, 2009. Everybody is welcome to participate.

The aim of the workshop is to strengthen the interactions between two different and very active areas of geometry: Integral geometry and Finsler geometry. Both areas are deeply related and use similar tools, like symplectic geometry, Gelfand and Crofton transforms, geometric measure theory, geometric inequalities and convex geometry. This workshop is therefore the perfect occasion to create fruitful collaborations between leading mathematicians in these fields.

We will focus on the following topics:

  • Kinematic formulas
  • Convex valuations
  • Hilbert's 4-th problem
  • Area and volume definitions

We are happy to announce the following speakers:
  • Judit Abardia (Barcelona)
  • Semyon Alesker (Tel Aviv)
  • Juan-Carlos Alvarez (Lille)
  • Dimitri Burago (Pennsylvania)
  • Patrick Foulon (Strasbourg)
  • Joseph Fu (Athens, Georgia)
  • Daniel Hug (Karlsruhe)
  • Matthias Reitzner (Wien)
  • Rolf Schneider (Freiburg)
  • Franz Schuster (Wien)
  • Gil Solanes (Barcelona)
  • Tony Thompson (Halifax)
  • Marc Troyanov (Lausanne)
  • Constantin Vernicos (Maynooth)

Gautier Berck (Fribourg)
Andreas Bernig (Fribourg)

There is no registration fee. If you need help with the hotel reservation,
please contact us.

For further information, please have a look at the web site of the workshop:

Please feel free to send this message to anyone who might be interested.

Best regards,

Gautier Berck (gautier.berck {-at-} unifr.ch)
Andreas Bernig (andreas.bernig {-at-} unifr.ch)