Infinitely many spacelike periodic trajectories on a class of Lorentz manifolds
Infinitesimal Blaschke conjectures on projective spaces
Integrable smooth planar billiards and evolutes.
Invariant distances and invariant differential metrics in locally convex spaces
Invariant two-forms for geodesic flows.
Isometries of spaces of convex compact subsets of globally non-positively Busemann curved spaces
We consider the Hausdorff metric on the space of compact convex subsets of a proper, geodesically complete metric space of globally non-positive Busemann curvature in which geodesics do not split, and characterize their surjective isometries. Moreover, an analogous characterization of the surjective isometries of the space of compact subsets of a proper, uniquely geodesic, geodesically complete metric space in which geodesics do not split is given.
Isoparametric hypersurfaces with less than four principal curvatures in a sphere
We characterize Clifford hypersurfaces and Cartan minimal hypersurfaces in a sphere by some properties of extrinsic shapes of their geodesics.
Isospectral hyperbolic surfaces have matching geodesics.