Journal of the
Korean Mathematical Society JKMS

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.