Quantizing Geodesics in K\"ahler and Sasaki Geometry
Differential Geometry
2026-03-19 v2 Complex Variables
Abstract
The space of K\"ahler potentials can be quantized through the classical Fubini-Study map, relating infinite-dimensional geometric structures to finite-dimensional symmetric spaces. We prove (exactly) when the Fubini-Study image of a geodesic line in the space of positive definite Hermitian matrices gives rise to a quasi-geodesic in the space of K\"ahler potentials. Furthermore, we introduce a quantization procedure for geodesics between potentials on normal K\"ahler varieties and show how this construction extends to the Sasaki setting.
Keywords
Cite
@article{arxiv.2603.01665,
title = {Quantizing Geodesics in K\"ahler and Sasaki Geometry},
author = {Gilles Courtois and Eleonora Di Nezza and Thomas Franzinetti},
journal= {arXiv preprint arXiv:2603.01665},
year = {2026}
}