Symmetric spaces as adjoint orbits and their geometries
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916161842577408 |
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| author | Cavenaghi, Leonardo F. Garcia, Carolina Grama, Lino Martin, Luiz San |
| author_facet | Cavenaghi, Leonardo F. Garcia, Carolina Grama, Lino Martin, Luiz San |
| contents | We realize specific classical symmetric spaces, like the semi-Kähler symmetric spaces discovered by Berger, as cotangent bundles of symmetric flag manifolds. These realizations enable us to describe these cotangent bundles' geodesics and Lagrangian submanifolds.
As a final application, we present the first examples of vector bundles over simply connected manifolds with nonnegative curvature that cannot accommodate metrics with nonnegative sectional curvature, even though their associated unit sphere bundles can indeed accommodate such metrics. Our examples are derived from explicit bundle constructions over symmetric flag spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09638 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symmetric spaces as adjoint orbits and their geometries Cavenaghi, Leonardo F. Garcia, Carolina Grama, Lino Martin, Luiz San Differential Geometry Symplectic Geometry We realize specific classical symmetric spaces, like the semi-Kähler symmetric spaces discovered by Berger, as cotangent bundles of symmetric flag manifolds. These realizations enable us to describe these cotangent bundles' geodesics and Lagrangian submanifolds. As a final application, we present the first examples of vector bundles over simply connected manifolds with nonnegative curvature that cannot accommodate metrics with nonnegative sectional curvature, even though their associated unit sphere bundles can indeed accommodate such metrics. Our examples are derived from explicit bundle constructions over symmetric flag spaces. |
| title | Symmetric spaces as adjoint orbits and their geometries |
| topic | Differential Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2302.09638 |