5 problems

Let $W$ be a closed, connected smooth manifold of dimension $n$, and for a smooth Riemannian metric $g$ on $W$ let … where $\operatorname{sys}(g)$ is the length of the shortest non…

A Zoll metric is a Riemannian metric for which all geodesics are periodic with a common period. The known examples include metrics of constant curvature on $S^m$ and $P^m$, the sta…

A Zoll metric of revolution is a metric of revolution all of whose geodesics are closed. A superintegrable (SI) system is an integrable Hamiltonian system admitting the additional…

Zoll metric uniqueness conjecture. The only Zoll metrics on the projective spaces over $\mathbb{C}$, $\mathbb{H}$ and $\mathbb{O}$ are the CROSSes.

Let the Matveev–Shevchishin superintegrable geodesic-flow systems be given on two-dimensional manifolds, and consider the corresponding metrics on closed manifolds. Matveev–Shevchi…