Real semisimple Lie groups and balanced metrics
Federico Giusti, Fabio Podestà
Abstract
Given any non-compact real simple Lie group \mathrm{G}_o of inner type and even dimension, we prove the existence of an invariant complex structure \mathrm{J} and a Hermitian balanced metric on \mathrm{G}_o and on any compact quotient \mathrm{M}= \Gamma\backslash\mathrm{G}_o , with \Gamma a cocompact lattice. We also prove that (\mathrm{M},\mathrm{J}) does not carry any pluriclosed metric, in contrast to the case of even dimensional compact Lie groups, which admit pluriclosed but not balanced metrics.
Topics & Concepts
Lie groupBackslashQuotientMathematicsLattice (music)Pure mathematicsReal formHermitian matrixSimple Lie groupCombinatoricsPhysicsAlgebra over a fieldAffine Lie algebraCurrent algebraAcousticsGeometry and complex manifoldsGeometric Analysis and Curvature FlowsAdvanced Algebra and Geometry