A paraK¨ahler Lie algebra is an even-dimensional Lie algebra g endowed with a pair $(J, g)$, where $J$ is a paracomplex structure and $g$ a pseudo-Riemannian metric, such that the fundamental 2-form $\Omega(X, Y) = g(X, JY)$ is symplectic. We completely classify left-invariant paraK¨ahler structures on four-dimensional Lie algebras and then study the geometry of their paraK¨ahler metric
Four-dimensional paraKahler Lie algebras: classification and geometry
CALVARUSO, Giovanni
2015-01-01
Abstract
A paraK¨ahler Lie algebra is an even-dimensional Lie algebra g endowed with a pair $(J, g)$, where $J$ is a paracomplex structure and $g$ a pseudo-Riemannian metric, such that the fundamental 2-form $\Omega(X, Y) = g(X, JY)$ is symplectic. We completely classify left-invariant paraK¨ahler structures on four-dimensional Lie algebras and then study the geometry of their paraK¨ahler metricFile in questo prodotto:
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