Pseudo-Riemannian Sasaki solvmanifolds
| Autor: | Conti, Diego, Rossi, Federico A., Dalmasso, Romeo Segnan |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | J. Korean Math. Soc. 60 (2023), No. 1, pp. 115-141 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4134/JKMS.j220232 |
| Popis: | We study a class of left-invariant pseudo-Riemannian Sasaki metrics on solvable Lie groups, which can be characterized by the property that the zero level set of the moment map relative to the action of some one-parameter subgroup $\{\exp tX\}$ is a normal nilpotent subgroup commuting with $\{\exp tX\}$, and $X$ is not lightlike. We characterize this geometry in terms of the Sasaki reduction and its pseudo-K\"ahler quotient under the action generated by the Reeb vector field. We classify pseudo-Riemannian Sasaki solvmanifolds of this type in dimension $5$ and those of dimension $7$ whose K\"ahler reduction in the above sense is abelian. Comment: 25 pages, 1 table. v2: corrected the Lie algebras appearing in Theorem 5.7 and Table 1; added Remark 5.9 concerning isomorphisms between Lie algebras in Table 1; typos corrected; presentation improved |
| Databáze: | arXiv |
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