Invariant Monge-Ampère equations on contactified para-Kähler manifolds
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910328881676288 |
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| author | Alekseevsky, Dmitri Manno, Gianni Moreno, Giovanni |
| author_facet | Alekseevsky, Dmitri Manno, Gianni Moreno, Giovanni |
| contents | We develop a method for describing invariant Monge-Ampère equations in the sense of V. Lychagin and T. Morimoto (MAE) on a homogeneous contact manifold $N$ of a semisimple Lie group $G$, which is the contactification of the homogeneous symplectic manifold $M = G/H = \mathrm{Ad}_G Z \subset \mathfrak{g}$, where $M$ is the adjoint orbit of a splittable closed element $Z $ of the Lie algebra $\mathfrak{g} = \mathrm{Lie}(G)$. The method is then applied to a ten-dimensional semisimple orbit $M$ of the exceptional Lie group $\mathsf{G}_2$ and a complete list of mutually non-equivalent MAEs on $N$ is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08315 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invariant Monge-Ampère equations on contactified para-Kähler manifolds Alekseevsky, Dmitri Manno, Gianni Moreno, Giovanni Differential Geometry 35B06, 58A20, 58J70 We develop a method for describing invariant Monge-Ampère equations in the sense of V. Lychagin and T. Morimoto (MAE) on a homogeneous contact manifold $N$ of a semisimple Lie group $G$, which is the contactification of the homogeneous symplectic manifold $M = G/H = \mathrm{Ad}_G Z \subset \mathfrak{g}$, where $M$ is the adjoint orbit of a splittable closed element $Z $ of the Lie algebra $\mathfrak{g} = \mathrm{Lie}(G)$. The method is then applied to a ten-dimensional semisimple orbit $M$ of the exceptional Lie group $\mathsf{G}_2$ and a complete list of mutually non-equivalent MAEs on $N$ is obtained. |
| title | Invariant Monge-Ampère equations on contactified para-Kähler manifolds |
| topic | Differential Geometry 35B06, 58A20, 58J70 |
| url | https://arxiv.org/abs/2402.08315 |