Notes on left-invariant metrics on the compact Lie group SU(3)

About left-invariant geometry and homogeneous pseudo-Riemannian Einstein structures on the Lie group SU(3)

This is a collection of notes on the properties of left-invariant metrics on the eight-dimensional compact group su(3).We recover the known examples (killing metric and jensen metric) in the riemannian case (signature (8,0)), as well as a gibbons et al example of signature (6,2), and we describe a new example (ie of signature (7,1)).In the latter case the associated metric is left-invariant, with isometry group su(3) x u(1), and has positive einstein constant.It seems to be the first example of a lorentzian homogeneous einstein metric on this compact manifold.