Mass from an Extrinsic Point of View
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917959263322112 |
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| author | de Sousa, Alexandre Girão, Frederico |
| author_facet | de Sousa, Alexandre Girão, Frederico |
| contents | We express the $q$-th Gauss-Bonnet-Chern mass of an immersed submanifold of Euclidean space as a linear combination of two terms: the total $(2q)$-th mean curvature and the integral, over the entire manifold, of the inner product between the $(2q+1)$-th mean curvature vector and the position vector of the immersion. As a consequence, we obtain, for each $q$, a geometric inequality that holds whenever the positive mass theorem (for the $q$-th Gauss-Bonnet-Chern mass) holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06782 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mass from an Extrinsic Point of View de Sousa, Alexandre Girão, Frederico Differential Geometry General Relativity and Quantum Cosmology We express the $q$-th Gauss-Bonnet-Chern mass of an immersed submanifold of Euclidean space as a linear combination of two terms: the total $(2q)$-th mean curvature and the integral, over the entire manifold, of the inner product between the $(2q+1)$-th mean curvature vector and the position vector of the immersion. As a consequence, we obtain, for each $q$, a geometric inequality that holds whenever the positive mass theorem (for the $q$-th Gauss-Bonnet-Chern mass) holds. |
| title | Mass from an Extrinsic Point of View |
| topic | Differential Geometry General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2403.06782 |