A review of compact geodesic orbit manifolds and the g.o. condition for $\SU(5)/\s(\U(2)\times \U(2))$
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910601828106240 |
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| author | Arvanitoyeorgos, Andreas Souris, Nikolaos Panagiotis Statha, Marina |
| author_facet | Arvanitoyeorgos, Andreas Souris, Nikolaos Panagiotis Statha, Marina |
| contents | Geodesic orbit manifolds (or g.o. manifolds) are those Riemannian manifolds $(M,g)$ whose geodesics are integral curves of Killing vector fields. Equivalently, there exists a Lie group $G$ of isometries of $(M,g)$ such that any geodesic $γ$ has the simple form $γ(t)=e^{tX}\cdot p$, where $e$ denotes the exponential map on $G$. The classification of g.o. manifolds is a longstanding problem in Riemannian geometry. In this brief survey, we present some recent results and open questions on the subject focusing on the compact case. In addition we study the geodesic orbit condition for the space $\SU(5)/\s(\U(2)\times \U(2))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08247 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A review of compact geodesic orbit manifolds and the g.o. condition for $\SU(5)/\s(\U(2)\times \U(2))$ Arvanitoyeorgos, Andreas Souris, Nikolaos Panagiotis Statha, Marina Differential Geometry 53C25, 53C30 Geodesic orbit manifolds (or g.o. manifolds) are those Riemannian manifolds $(M,g)$ whose geodesics are integral curves of Killing vector fields. Equivalently, there exists a Lie group $G$ of isometries of $(M,g)$ such that any geodesic $γ$ has the simple form $γ(t)=e^{tX}\cdot p$, where $e$ denotes the exponential map on $G$. The classification of g.o. manifolds is a longstanding problem in Riemannian geometry. In this brief survey, we present some recent results and open questions on the subject focusing on the compact case. In addition we study the geodesic orbit condition for the space $\SU(5)/\s(\U(2)\times \U(2))$. |
| title | A review of compact geodesic orbit manifolds and the g.o. condition for $\SU(5)/\s(\U(2)\times \U(2))$ |
| topic | Differential Geometry 53C25, 53C30 |
| url | https://arxiv.org/abs/2409.08247 |