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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.16018 |
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| _version_ | 1866911218272305152 |
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| author | Choudhury, Shouvik Datta |
| author_facet | Choudhury, Shouvik Datta |
| contents | We formalize the ``metric bundle'' viewpoint by defining, for any smooth $n$--manifold $M$, the open fiberwise cones $\mathcal{G}^{p,q}\subset S^2\Tstar M$ of nondegenerate symmetric bilinear forms with fixed signature $(p,q)$, and we package \emph{multi\-metric} (``polymetric'') geometries as sections of finite products of such cones. This framework subsumes Riemannian and pseudo-Riemannian metrics, and admits clean extensions to conformal, densitized, Finsler, and sub-Riemannian structures. It also interfaces correctly with families index theory (Atiyah--Singer), equivariant/groupoid settings, and coarse/KK-theory. On compact $M$ the Riemannian space of metrics is convex (hence contractible), giving a transparent base for moduli and deformation theory |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16018 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Bundles of Metrics and Polymetrics: A Generalization Choudhury, Shouvik Datta Differential Geometry We formalize the ``metric bundle'' viewpoint by defining, for any smooth $n$--manifold $M$, the open fiberwise cones $\mathcal{G}^{p,q}\subset S^2\Tstar M$ of nondegenerate symmetric bilinear forms with fixed signature $(p,q)$, and we package \emph{multi\-metric} (``polymetric'') geometries as sections of finite products of such cones. This framework subsumes Riemannian and pseudo-Riemannian metrics, and admits clean extensions to conformal, densitized, Finsler, and sub-Riemannian structures. It also interfaces correctly with families index theory (Atiyah--Singer), equivariant/groupoid settings, and coarse/KK-theory. On compact $M$ the Riemannian space of metrics is convex (hence contractible), giving a transparent base for moduli and deformation theory |
| title | Universal Bundles of Metrics and Polymetrics: A Generalization |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2510.16018 |