Tamaru's TALK (Spain 2019)

Data

Geometry of homogeneous hypersurfaces in noncompact symmetric spaces.
Symmetry and shape - Celebrating the 60th birthday of Prof. J. Berndt (Universidade de Santiago de Compostela, Spain), 2019/09/28.

Abstract

According to the results by Berndt-Bruck and Berndt-Tamaru, cohomogeneity one actions on irreducible Riemannian symmetric spaces of noncompact type can be divided into the following three classes: (K) there is a unique singular orbit, (A) all orbits are regular and there is a unique minimal orbit, or (N) all orbits are isometrically congruent to each other. Note that regular orbits of these actions are precisely homogeneous hypersurfaces. In this talk, we review several recent results on geometry of these homogeneous hypersurfaces, including the classification problems, intrinsic geometry, and extrinsic geometry.

Files

• The slide of the talk can be found at the conference webpage here.