Minimal geodescis

12.10.2023, 16:15  –  Raum 0.14
Forschungsseminar Differentialgeometrie

Bernd Ammann (Regensburg)

A geodesic \(c : \mathbf{R}\to M\) is called minimal if a lift to the universal covering globally minimizes distance. On the 2-dimensional torus with an arbitrary Riemannian metric there are uncountably many minimal geodesic. In dimension at least 3, there may be very few minimal geodesics. If \(M\) is closed, Bangert has shown that the number of geometrically distinct minimal geodesics is bounded below by the first Betti number \(b_1\). In joint work with Clara Löh, we improve Bangert’s lower bound and we show that this number is at least \(b_1^2 + 2b_1\).