Geometric Properties and Distance Inequalities on Grassmannians
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912162118631424 |
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| author | Tam, Tin-Yau Wang, Xiang Xiang |
| author_facet | Tam, Tin-Yau Wang, Xiang Xiang |
| contents | In this paper we obtain inequalities for the geometric mean of elements in the Grassmannians. These inequalities reflect the elliptic geometry of the Grassmannians as Riemannian manifolds. These include Semi-Parallelogram Law, Law of Cosines and geodesic triangle inequalities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15161 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric Properties and Distance Inequalities on Grassmannians Tam, Tin-Yau Wang, Xiang Xiang Differential Geometry In this paper we obtain inequalities for the geometric mean of elements in the Grassmannians. These inequalities reflect the elliptic geometry of the Grassmannians as Riemannian manifolds. These include Semi-Parallelogram Law, Law of Cosines and geodesic triangle inequalities. |
| title | Geometric Properties and Distance Inequalities on Grassmannians |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2412.15161 |