講演アブストラクト

For some totally geodesic submanifolds $N$ in noncompact symmetric spaces $M$, any isometric action on $N$ can be extended to an isometric action on $M$. We call this the canonical extension. In this talk, I would like to explain that the canonical extension provides many interesting examples of isometric actions on noncompact symmetric spaces of higher rank, and plays important roles for the study of cohomogeneity one actions (with Jurgen Berndt) and of hyperpolar foliations (with Jurgen Berndt and Jose Carlos Diaz-Ramos).