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.
"Examples of austere orbits of the isotropy representations for semisimple pseudo-Riemannian symmetric spaces." Tohoku Math. J. (2) 71 (3) 397 - 424, 2019. https://doi.org/10.2748/tmj/1568772178