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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.15643 |
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| _version_ | 1866910223530196992 |
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| author | Su, Zhe |
| author_facet | Su, Zhe |
| contents | We introduce a de Rham-Hodge framework induced by a vector field on a compact, oriented smooth manifold. By utilizing a vector field induced isomorphism on differential forms, we define a vector field induced Hodge $L^2$-inner product, codifferential, and Hodge Laplacian on differential forms. We then establish the resulting de Rham-Hodge theory for closed manifolds and extend it to manifolds with boundary by imposing certain vector field induced boundary conditions. We also include some remarks on this resulting framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15643 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A vector field induced de Rham-Hodge theory on manifolds Su, Zhe Differential Geometry We introduce a de Rham-Hodge framework induced by a vector field on a compact, oriented smooth manifold. By utilizing a vector field induced isomorphism on differential forms, we define a vector field induced Hodge $L^2$-inner product, codifferential, and Hodge Laplacian on differential forms. We then establish the resulting de Rham-Hodge theory for closed manifolds and extend it to manifolds with boundary by imposing certain vector field induced boundary conditions. We also include some remarks on this resulting framework. |
| title | A vector field induced de Rham-Hodge theory on manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.15643 |