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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.16166 |
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| _version_ | 1866908548136435712 |
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| author | Eschenburg, Jost-Hinrich Heintze, Ernst Quast, Peter |
| author_facet | Eschenburg, Jost-Hinrich Heintze, Ernst Quast, Peter |
| contents | We give a new proof of a theorem of Loos stating that a Riemannian symmetric space X with rectangular unit lattice is a symmetric R-space. For this we construct explicitly an isometric extrinsically symmetric embedding of X in a Euclidean space which reveals X as a standardly embedded symmetric R-space. We further determine the root systems, Euclidean root data, fundamental groups and eigenvalues of the Laplacian of symmetric spaces with rectangular unit lattice in a direct way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16166 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetric Spaces with Rectangular Unit Lattices, Revisited Eschenburg, Jost-Hinrich Heintze, Ernst Quast, Peter Differential Geometry 53C35, 53C40 We give a new proof of a theorem of Loos stating that a Riemannian symmetric space X with rectangular unit lattice is a symmetric R-space. For this we construct explicitly an isometric extrinsically symmetric embedding of X in a Euclidean space which reveals X as a standardly embedded symmetric R-space. We further determine the root systems, Euclidean root data, fundamental groups and eigenvalues of the Laplacian of symmetric spaces with rectangular unit lattice in a direct way. |
| title | Symmetric Spaces with Rectangular Unit Lattices, Revisited |
| topic | Differential Geometry 53C35, 53C40 |
| url | https://arxiv.org/abs/2509.16166 |