# Tagged Questions

**4**

votes

**0**answers

222 views

### Symmetric matrices and Hilbert's fourth problem

From the analytic viewpoint, the Busemann-Pogorelov solution of Hilbert's fourth problem is summarized in the following result:
Theorem. All straight lines are extremals of the variational problem
$$
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**1**

vote

**1**answer

258 views

### Reversibility vs geodesic reversibility for Finsler metrics on the two-sphere

Problem. To give a concrete example of a geodesically reversible Finsler metric on the two-sphere that is not just the sum of a reversible Finsler metric and an exact $1$-form.
Some background may be ...

**5**

votes

**1**answer

196 views

### Forms satisfying the zero-energy condition on the projective plane

Theorem (Michel). A $1$-form on the projective plane is exact if and only if its integral over any projective line is equal to zero.
Is there a simple proof of this result due, I think, to R. Michel ...

**2**

votes

**1**answer

360 views

### On the generalized Radon transform and currents

Given a family of hypersurfaces $H_{t,p} = $ {$x \in \mathbb{R}^n \mid g(x,p) = t $} one defines a generalized Radon transform $R$ of a function $u \colon \mathbb{R}^n \to \mathbb{R}$ as
$$
R[u] ...