Warped product metrics on hyperbolic and complex hyperbolic manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909800200142848 |
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| author | Minemyer, Barry |
| author_facet | Minemyer, Barry |
| contents | In this paper we study warped-product metrics on manifolds of the form $X \setminus Y$, where $X$ denotes either $\mathbb{H}^n$ or $\mathbb{C} \mathbb{H}^n$, and $Y$ is a totally geodesic submanifold with arbitrary codimension. The main results that we prove are curvature formulas for these metrics on $X \setminus Y$ expressed in spherical coordinates about $Y$. We also discuss past and potential future applications of these formulas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_15553 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Warped product metrics on hyperbolic and complex hyperbolic manifolds Minemyer, Barry Differential Geometry Metric Geometry In this paper we study warped-product metrics on manifolds of the form $X \setminus Y$, where $X$ denotes either $\mathbb{H}^n$ or $\mathbb{C} \mathbb{H}^n$, and $Y$ is a totally geodesic submanifold with arbitrary codimension. The main results that we prove are curvature formulas for these metrics on $X \setminus Y$ expressed in spherical coordinates about $Y$. We also discuss past and potential future applications of these formulas. |
| title | Warped product metrics on hyperbolic and complex hyperbolic manifolds |
| topic | Differential Geometry Metric Geometry |
| url | https://arxiv.org/abs/2307.15553 |