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The space of left-invariant metrics on a Lie group.
Seminar, King's College London,
We study the space of left-invariant Riemannian metrics
on a Lie group up to isometry and scaling.
Such space can be identified with the orbit space
of certain isometric action on a symmetric space of noncompact type,
and hence the theory of homogeneous submanifold could be applicable.
In this talk, we describe some Lie groups whose spaces
of left-invariant metrics are small, that is,
the corresponding isometric actions are transitive or of cohomogeneity one.
This talk is based on a joint work with Hiroshi Kodama and Atsushi Takahara.