Talk:Finsler manifold

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 Field:  Geometry

On Finsler-geometry related articles[edit]

This page calls for elaboration by the specialists. It might also be beneficial to create a handful of related articles to cover the central features of Finsler geometry. Here is a crude list of possible topics:

  • Own article for Minkowski norms with more explanation and examples.
  • Article on (semi)spray structures.
  • Article on Lagrangian geometry.
  • Article on nonlinear (spray) connections on TM\0.
  • Article(s) on different linear Finsler connections (Berwald, Cartan, Chern, Hashiguchi) on the pullback bundle.

Here is another list for possible new sections within this page:

  • Induced geometric structures (Sasaki metric and symplectic form on TM\0 and contact structure on SM )
  • Finsler manifolds as (quasi)metric spaces
  • Non-Riemannian curvatures and classification of Finsler manifolds (Berwald, Landberg, Randers,...)
  • Results from Riemannian geometry that hold for Finsler manifolds

Lapasotka (talk) 19:54, 17 August 2009 (UTC)

This looks like an excellent project. I have some thoughts, in no particular order:
  • Note that there is something on Finsler structures at the unit tangent bundle article, although I only stated the Sasakian property for the Riemannian case. If incorporated here, it should probably be developed in concert with that article.
  • The various associated connections can be incorporated into the Category:Connection (mathematics).
  • The geodesic spray for a Riemannian metric is discussed briefly at geodesic. I do think at the very least that Finsler structures should be represented in that article, although it should probably be treated separately from the Riemannian case, per WP:UNDUE WEIGHT considerations. There is a longer article on geodesics as Hamiltonian flows which could be linked up with this. Sławomir Biały (talk) 14:33, 19 August 2009 (UTC)

Progress report[edit]

I have started a proper article at spray (mathematics), which is hopefully mostly correct. I have also added some content on the geodesic spray associated to a non-linear connection to geodesic. Sławomir Biały (talk) 22:10, 20 August 2009 (UTC)

Minkowski norm[edit]

What is a Minkowski norm? "Minkowski norm" redirects to "Minkowski space". But the 'norm' associated to the Minkowski inner product is obviously not the thing meant in this article. --Trigamma (talk) 19:15, 1 July 2010 (UTC)