Tamaru's WEB PAGERESEARCHTALK

講演アブストラクト

講演情報

アブストラクト

Left-invariant Riemannian metrics on Lie groups have provided many interesting examples of homogeneous Einstein and Ricci soliton manifolds. In general, it is not easy to examine whether a given Lie group admit such distinguished metrics or not. In this talk, I will explain our approach from submanifold geometry. In particular, for three-dimensional solvable Lie groups, the existence and nonexistence of left-invariant Ricci solitons have a nice correspondence with the geometry of cohomogeneity one actions on some noncompact symmetric space. I will also mention some higher-dimensional examples and a pseudo-Riemannian version.

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