University thesis:
Dissertation, Universität Freiburg, 2019
Footnote:
Description:
Abstract: This thesis studies stable, closed geodesics on a Ricci-flat Kummer K3 surface. The motivation for counting stable, closed geodesics is explained and put into the context of comparison geometry. Building on estimates due to R. Kobayashi, restrictions on stable, closed geodesics on arbitrary Kummer K3s are derived. Then, in a complementary effort, isometry and special Lagrangian arguments are put forward to construct concrete, stable closed geodesics on a highly symmetric Kummer K3. This gives a partial affirmative answer to a conjecture put forward by P. Gao and M. Douglas, namely that any Ricci-flat, compact Calabi-Yau manifold will always carry stable, closed geodesics