Lines in the space of Kähler metrics
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866914328075042816 |
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| author | Darvas, Tamás McCleerey, Nicholas |
| author_facet | Darvas, Tamás McCleerey, Nicholas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17375 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lines in the space of Kähler metrics Darvas, Tamás McCleerey, Nicholas Differential Geometry Complex Variables 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. |
| title | Lines in the space of Kähler metrics |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2507.17375 |