Hermann type actions on a pseudo-Riemannian symmetric space

TL;DR

This paper explores the geometry of orbits in pseudo-Riemannian symmetric spaces, focusing on isotropy and Hermann type actions, revealing new structural insights through complexification and specific examples.

Contribution

It introduces a detailed analysis of Hermann type actions on pseudo-Riemannian symmetric spaces, highlighting new geometric structures and orbit properties.

Findings

Complexified action reveals orbit geometry

Identification of interesting structures via special Hermann actions

Enhanced understanding of orbit geometry in pseudo-Riemannian spaces

Abstract

We first investigate the geometry of orbits of the isotropy action on a semi-simple pseudo-Riemannian symmetric space by investigating the complexified action. Next we investigate the geometry of the orbits of Hermann type actions on the symmetric spaces. By considering two special Hermann type actions on the symmetric space, we recognize an interesting structure of the symmetric space.