Gauss-Bonnet for Form Curvatures
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909303140515840 |
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| author | Knill, Oliver |
| author_facet | Knill, Oliver |
| contents | We look at curvatures that are supported on k-dimensional parts of a simplicial complex G. These curvature all satisfy the Gauss-Bonnet theorem, provided that the k-dimensional simplices cover $G$. Each of these curvatures can be written as an expectation of Poincare-Hopf indices. Linear or non-linear wave dynamics with discrete or continuous time allow to deform these curvatures while keeping the Gauss-Bonnet property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01425 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gauss-Bonnet for Form Curvatures Knill, Oliver Combinatorics 05Cxx, 68R10, 53Axx We look at curvatures that are supported on k-dimensional parts of a simplicial complex G. These curvature all satisfy the Gauss-Bonnet theorem, provided that the k-dimensional simplices cover $G$. Each of these curvatures can be written as an expectation of Poincare-Hopf indices. Linear or non-linear wave dynamics with discrete or continuous time allow to deform these curvatures while keeping the Gauss-Bonnet property. |
| title | Gauss-Bonnet for Form Curvatures |
| topic | Combinatorics 05Cxx, 68R10, 53Axx |
| url | https://arxiv.org/abs/2409.01425 |