J. Korean Math. Soc. 2023; 60(1): 115-141
Online first article December 12, 2022 Printed January 1, 2023
https://doi.org/10.4134/JKMS.j220232
Copyright © The Korean Mathematical Society.
Diego Conti, Federico A. Rossi, Romeo Segnan Dalmasso
Universit\`a di Milano Bicocca; Universit\`a degli studi di Perugia; Universit\`a di Milano Bicocca
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.
Keywords: Sasaki, indefinite metric, contact reduction, standard Lie algebra
MSC numbers: Primary 53C25; Secondary 53D20, 53C50, 22E25
Supported by: This work was financially supported by GNSAGA of INdAM.
2023; 60(5): 1135-1136
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