Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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D. Conti - F. A. Rossi - R. Segnan Dalmasso

Pseudo-Riemannian Sasaki solvmanifolds

created by rossi on 14 Apr 2022



Inserted: 14 apr 2022
Last Updated: 14 apr 2022

Year: 2022

ArXiv: 2204.06294 PDF


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.

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