Path Connectivity of Anosov Metrics on Surfaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914251915919360 |
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| author | Guglielmo, Guilherme Brandão Ruggiero, R. |
| author_facet | Guglielmo, Guilherme Brandão Ruggiero, R. |
| contents | We construct a class of Riemannian metrics in closed surfaces of genus greater than one, having Anosov geodesic flows, and some regions of positive curvature, such that for each such surface, there exists a smooth curve of conformal deformations that preserves the Anosov property and connects the surface with a Riemannian metric of negative curvature. The conformal deformation does not arise from geometric flows like the Ricci flow, since it is known that such flows might generate conjugate points in the presence of points of positive curvature in the surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08656 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Path Connectivity of Anosov Metrics on Surfaces Guglielmo, Guilherme Brandão Ruggiero, R. Dynamical Systems Differential Geometry 53C44 (primary), 37D40, 53D25 (secondary) We construct a class of Riemannian metrics in closed surfaces of genus greater than one, having Anosov geodesic flows, and some regions of positive curvature, such that for each such surface, there exists a smooth curve of conformal deformations that preserves the Anosov property and connects the surface with a Riemannian metric of negative curvature. The conformal deformation does not arise from geometric flows like the Ricci flow, since it is known that such flows might generate conjugate points in the presence of points of positive curvature in the surface. |
| title | Path Connectivity of Anosov Metrics on Surfaces |
| topic | Dynamical Systems Differential Geometry 53C44 (primary), 37D40, 53D25 (secondary) |
| url | https://arxiv.org/abs/2601.08656 |