Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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PSEUDO-RIEMANNIAN SASAKI SOLVMANIFOLDS

  • Diego Conti (Dipartimento di Matematica e Applicazioni Universita di Milano Bicocca) ;
  • Federico A. Rossi (Dipartimento di Matematica e Informatica Universita degli studi di Perugia) ;
  • Romeo Segnan Dalmasso (Dipartimento di Matematica e Applicazioni Universita di Milano Bicocca)
  • Received : 2022.05.13
  • Accepted : 2022.09.19
  • Published : 2023.01.01
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Abstract

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-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.

Keywords

Acknowledgement

This work was financially supported by GNSAGA of INdAM.

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