Kahler metrics whose geodesics are circles
Vladlen Timorin
Abstract
We classify all Kahler metrics in an open subset of C2 whose real geodesics are circles. All such metrics are equivalent (via complex projective transformations) to Fubini metrics (i.e. to Fubini-Study metric on CP2 restricted to an affine chart, to the complex hyperbolic metric in the unit ball model or to the Euclidean metric).
Create a lesson
Related papers
Topological and spectral rigidity of hypersurface Zoll manifolds
Gustavo Martins
Stationary varifolds with singularities II
Camillo De Lellis, Jonas Hirsch, Zachary Lihn et al.
Alexandrov's Theorem for Integral Varifolds and Applications to Geometric Inequalities
Mitchell Gaudet
Deformations of harmonic maps with conical singularities
Dominik Gutwein, Thibault Langlais
The isoperimetric inequality and CMC hypersurfaces in Cartan-Hadamard manifolds
Shibing Chen, Mohammad Ghomi, Peng Wang
Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles II
Wangjian Jian, Jian Song