Talk:Finsler manifold

On Finsler-geometry related articles

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

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

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)