The zeta-determinants and anlaytic torsion of a metric mapping torus
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910519746625536 |
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| author | Lee, Yoonweon |
| author_facet | Lee, Yoonweon |
| contents | We use the BFK-gluing formula for zeta-determinants to compute the zeta-determinant and analytic torsion of a metric mapping torus induced from an isometry. As applications, we compute the zeta-determinants of the Laplacians defined on a Klein bottle ${\mathbb K}$ and some compact co-Kähler manifold ${\mathbb T}_φ$. We also show that a metric mapping torus and a Riemannian product manifold with a round circle have the same heat trace asymptotic expansions. We finally compute the analytic torsion of a metric mapping torus for the Witten deformed Laplacian and recover the result of J. Marcsik in \cite{Ma}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06609 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The zeta-determinants and anlaytic torsion of a metric mapping torus Lee, Yoonweon Differential Geometry 58J52 We use the BFK-gluing formula for zeta-determinants to compute the zeta-determinant and analytic torsion of a metric mapping torus induced from an isometry. As applications, we compute the zeta-determinants of the Laplacians defined on a Klein bottle ${\mathbb K}$ and some compact co-Kähler manifold ${\mathbb T}_φ$. We also show that a metric mapping torus and a Riemannian product manifold with a round circle have the same heat trace asymptotic expansions. We finally compute the analytic torsion of a metric mapping torus for the Witten deformed Laplacian and recover the result of J. Marcsik in \cite{Ma}. |
| title | The zeta-determinants and anlaytic torsion of a metric mapping torus |
| topic | Differential Geometry 58J52 |
| url | https://arxiv.org/abs/2407.06609 |