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)[reply]

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)[reply]

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)[reply]

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)[reply]