Quantizing Geodesics in Kähler and Sasaki Geometry
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918395008516096 |
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| author | Courtois, Gilles Di Nezza, Eleonora Franzinetti, Thomas |
| author_facet | Courtois, Gilles Di Nezza, Eleonora Franzinetti, Thomas |
| contents | The space of Kähler 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 Kähler potentials. Furthermore, we introduce a quantization procedure for geodesics between potentials on normal Kähler varieties and show how this construction extends to the Sasaki setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01665 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantizing Geodesics in Kähler and Sasaki Geometry Courtois, Gilles Di Nezza, Eleonora Franzinetti, Thomas Differential Geometry Complex Variables 32Q15, 53C25, 58B20, 53D50, 54E40 The space of Kähler 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 Kähler potentials. Furthermore, we introduce a quantization procedure for geodesics between potentials on normal Kähler varieties and show how this construction extends to the Sasaki setting. |
| title | Quantizing Geodesics in Kähler and Sasaki Geometry |
| topic | Differential Geometry Complex Variables 32Q15, 53C25, 58B20, 53D50, 54E40 |
| url | https://arxiv.org/abs/2603.01665 |