Cut loci of Berger type Lorentzian structures
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909602627452928 |
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| author | Podobryaev, A. V. |
| author_facet | Podobryaev, A. V. |
| contents | Consider the deformation of the standard Lorentzian metric on the anti de-Sitter space along the fibers of the Hopf fibration. We study the universal covering of this Lorentzian manifold to exclude a priori presence of time-like cycles. We describe the sets attainable by admissible curves and study the question of the existence of the longest arcs. Next, we investigate Lorentzian geodesics for optimality: we find the cut time and the cut locus. As a geometric application we compute the injectivity radius of the corresponding Lorentzian manifold. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_03514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cut loci of Berger type Lorentzian structures Podobryaev, A. V. Differential Geometry 53C50, 53C30, 49J15 Consider the deformation of the standard Lorentzian metric on the anti de-Sitter space along the fibers of the Hopf fibration. We study the universal covering of this Lorentzian manifold to exclude a priori presence of time-like cycles. We describe the sets attainable by admissible curves and study the question of the existence of the longest arcs. Next, we investigate Lorentzian geodesics for optimality: we find the cut time and the cut locus. As a geometric application we compute the injectivity radius of the corresponding Lorentzian manifold. |
| title | Cut loci of Berger type Lorentzian structures |
| topic | Differential Geometry 53C50, 53C30, 49J15 |
| url | https://arxiv.org/abs/2505.03514 |