Questions tagged [finsler]

For questions about Finsler geometry.

8 questions with no upvoted or accepted answers
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Geodesics of non-smooth Finsler structure, or non-smooth Lagrange problem

I need to find the geodesics of a certain Finsler structure on $\mathbb R^n$. The structure is determined by quite nice $\ell^1$-like norms on tangent spaces, so that it is reversible. However the ...
3
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102 views

Existence of connections in a vector bundle whose parallel transport preserves a function on a total space

Let $p:E \to M$ be a vector bundle over a smooth manifold $M$, $M\times 0$ be the image of its zero section of $p$, $\mathcal{X}(M)$ be the space of vector fields on $M$, and $\Gamma(E)$ be the space ...
3
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72 views

How to find geodesics in a Randers spaces?

Consider a Randers space $(M,F)$ that is the solution of the zermelo's navigation problem associated to a wind $W$ which is homothety; $\mathcal{L}_Wh=\sigma h$, $\delta$ constant, on a Riemannian ...
2
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Minkowski functional on infinite dimensional vector spaces

In finite dimensional Finsler geometry, we define Minkowski functional on tangent spaces that are finite dimensional vector spaces. The definition of Minkowski functional can be generalized to ...
2
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0answers
128 views

Exponential Map for non-smooth Finsler manifolds

Context If I'm interested in studying reversible Finsler manifolds which do not have the strong convexity of the Hessian property (that is the Finsler function is a regular norm on every tangent ...
1
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52 views

Second variation in saddle Finsler surface

Setting : Consider a two dimensional surface in $ (\mathbb{R}^n,\|\ \|)$. Here we define a function $f: \mathbb{R}^n\rightarrow \mathbb{R}^n$ s.t. $L(v)(X)=\langle f(v),X\rangle$ where $\langle\ ,\...
1
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54 views

What happens if in Randers metric the norm of the wind is not less than 1

One way to define the Randers metric is using the data $(h,W)$ associated to the Zermelo problem. Here $h$ is the Riemannian metric and $W$ is the wind. In order to define the Randers metric we must ...
0
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98 views

Angle between two vectors in a Minkowski (Finsler) space!

Given a Minkowski (or Finsler) space $(V,F)$, I am wondering how to define the angle between two vectors $w$ and $v$. I first thought it must be as $$\cos\theta(w,v)=\frac{g_w(w,v)}{\sqrt{g_w(w,w)g_w(...