Tamaru's TALK (Queensland 2019)
Data
On the moduli spaces of left-invariant geometric structures.
Workshop on geometric analysis and homogeneous geometry
(The University of Queensland, Australia),
2019/06/24-28.
Abstract
The set of some type of left-invariant geometric structures on a given Lie group
forms a symmetric space in many cases.
The orbit space of the action of scaling and the automorphism group of the Lie group
on this symmetric space can be regarded as the moduli space of the geometric structures.
This gives a kind of generalization of Milnor frames
for left-invariant Riemannian metrics on three-dimensional unimodular Lie groups.
In this talk,
we consider these moduli spaces,
mainly on left-invariant Riemannian metrics,
but also for left-invariant pseudo-Riemannian metrics and for left-invariant symplectic structures.
They can be applied to the study of
the existence and nonexistence of some distinguished left-invariant geometric structures.
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