Finsler space | Wikipedia audio article
Channel: wikipedia tts
Date: 29/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Finsler_manifold


00:01:35 1 Definition
00:03:34 2 Examples
00:04:37 2.1 Randers manifolds
00:04:51 2.2 Smooth quasimetric spaces
00:05:26 3 Geodesics
00:06:37 3.1 Canonical spray structure on a Finsler manifold
00:08:59 3.2 Uniqueness and minimizing properties of geodesics
00:11:07 4 Notes
00:13:21 5 References
00:19:59 6 External links
00:22:28 Uniqueness and minimizing properties of geodesics
00:23:12 x and γ'(0)



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SUMMARY
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In mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold M where a (possibly asymmetric) Minkowski functional F(x,−) is provided on each tangent space TxM, allowing to define the length of any smooth curve γ : [a,b] → M as

  
    
      
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    {\displaystyle L(\gamma )=\int _{a}^{b}F(\gamma (t),{\dot {\gamma }}(t))\,\mathrm {d} t.}
  Finsler manifolds are more general than Riemannian manifolds since the tangent norms need not be induced by inner products.
Every Finsler manifold becomes an intrinsic quasimetric space when the distance between two points is defined as the infimum length of the curves that join them.
Élie Cartan (1933) named Finsler manifolds after Paul Finsler, who studied this geometry in his dissertation (Finsler 1918).