Riemannian Geometry of $G_2$-type Real Flag Manifolds
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917560991088640 |
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| author | Grajales, Brian Rondón, Gabriel Saavedra, Julieth |
| author_facet | Grajales, Brian Rondón, Gabriel Saavedra, Julieth |
| contents | In this paper, we investigate homogeneous Riemannian geometry on real flag manifolds of the split real form of $\mathfrak{g}_2$. We characterize the metrics that are invariant under the action of a maximal compact subgroup of $G_2.$ Our exploration encompasses the analysis of g.o. metrics and equigeodesics on the $\mathfrak{g}_2$-type flag manifolds. Additionally, we explore the Ricci flow for the case where the isotropy representation has no equivalent summands, employing techniques from the qualitative theory of dynamical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02805 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Riemannian Geometry of $G_2$-type Real Flag Manifolds Grajales, Brian Rondón, Gabriel Saavedra, Julieth Differential Geometry Dynamical Systems 22F30, 53C30 In this paper, we investigate homogeneous Riemannian geometry on real flag manifolds of the split real form of $\mathfrak{g}_2$. We characterize the metrics that are invariant under the action of a maximal compact subgroup of $G_2.$ Our exploration encompasses the analysis of g.o. metrics and equigeodesics on the $\mathfrak{g}_2$-type flag manifolds. Additionally, we explore the Ricci flow for the case where the isotropy representation has no equivalent summands, employing techniques from the qualitative theory of dynamical systems. |
| title | Riemannian Geometry of $G_2$-type Real Flag Manifolds |
| topic | Differential Geometry Dynamical Systems 22F30, 53C30 |
| url | https://arxiv.org/abs/2401.02805 |