Work

$$\varvec{\eta }$$-Einstein Sasakian Lie algebras

Year: 2026

Type: article

Abstract: We study $$\eta $$ η -Einstein Sasakian structures on Lie algebras, that is, Sasakian structures whose associated Ricci tensor satisfies an Einstein-like condition. We divide into the cases in which the Lie algebra’s centre is non-trivial (and necessarily one-dimensional) from those where it is zero. In the former case we show that any Sasakian structure on a unimodular Lie algebra is $$\eta $$ η -Einstein. As for centreless Sasakian Lie algebras, we devise a complete characterisation under certain dimensional assumptions regarding the action of the Reeb vector. Using this result, together with the theory of normal j -algebras and modifications of Hermitian Lie algebras, we construct new examples of $$\eta $$ η -Einstein Sasakian Lie algebras and solvmanifolds, and provide effective restrictions for their existence.

Source: manuscripta mathematica

DOI: 10.1007/s00229-026-01692-9

Authors: Adrián Andrada, Simon G. Chiossi, Alberth J. Núñez Sullca

Institutions: Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad Nacional de Córdoba, Universidade Federal Fluminense

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Universidade Federal Fluminense