Examples of austere orbits of the isotropy representations for semisimple pseudo-Riemannian symmetric spaces

TL;DR

This paper characterizes austere orbits of isotropy representations in semisimple pseudo-Riemannian symmetric spaces, providing a criterion based on root systems and presenting explicit examples.

Contribution

It introduces an equivalent condition for austere orbits using restricted root system theory and constructs explicit examples of such orbits.

Findings

Established a criterion for austere orbits in terms of root systems

Provided explicit examples of austere orbits

Connected austere submanifolds with isotropy representations in pseudo-Riemannian symmetric spaces

Abstract

Harvey-Lawson and Anciaux introduced the notion of austere submanifolds in pseudo-Riemannian geometry. We give an equivalent condition for an orbit of the isotropy representations for semisimple pseudo-Riemannian symmetric space to be an austere submanifold in a pseudo-sphere in terms of restricted root system theory with respect to Cartan subspaces. By using the condition we give examples of austere orbits.