We study a class of left-invariant pseudo-Riemannian Sasaki metrics on solvable Lie groups, which can be characterized by the prop-erty 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-Kähler 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 Kähler reduction in the above sense is abelian.
Conti, D., Rossi, F., Segnan Dalmasso, R. (2023). Pseudo-Riemannian Sasaki solvmanifolds. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 60(1), 115-141 [10.4134/JKMS.j220232].
Pseudo-Riemannian Sasaki solvmanifolds
Rossi, FA;Segnan Dalmasso, R
2023
Abstract
We study a class of left-invariant pseudo-Riemannian Sasaki metrics on solvable Lie groups, which can be characterized by the prop-erty 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-Kähler 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 Kähler reduction in the above sense is abelian.File | Dimensione | Formato | |
---|---|---|---|
Conti-2023-J Korean Math Soc-AAM.pdf
accesso aperto
Descrizione: Article
Tipologia di allegato:
Author’s Accepted Manuscript, AAM (Post-print)
Licenza:
Altro
Dimensione
455.13 kB
Formato
Adobe PDF
|
455.13 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.