Lines in the space of Kähler metrics
Abstract
Abstract We establish a Ross–Witt Nyström correspondence for weak geodesic lines in the (completed) space of Kähler metrics. We construct a wide range of weak geodesic lines on arbitrary projective Kähler manifolds that are not generated by holomorphic vector fields, in the process disproving a folklore conjecture popularized by Berndtsson. Remarkably, some of these weak geodesic lines turn out to be smooth. In the case of Riemann surfaces, our results can be significantly sharpened. Finally, we investigate the validity of Euclid’s fifth postulate for the space of Kähler metrics.
Fields of Study & Subjects
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Advanced Differential Geometry Research
Publication details
- Journal / source
- Mathematische Annalen
- Volume
- 396
- Issue
- 2
- Publication date
- 15 September 2026
- Language
- EN