講演アブストラクト

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.