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.
Articolo in rivista - Articolo scientifico
contact reduction; indefinite metric; Sasaki; standard Lie algebra;
English
1-gen-2023
2023
60
1
115
141
open
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/401736
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