Classification of Cartan embeddings which are austere submanifolds (Q2134173)

Austere submanifolds where introduced by \textit{R. Harvey} and \textit{H. B. Lawson} [Acta Math. 148, 47--157 (1982; Zbl 0584.53021)] in connection with their study of calibrated geometries. In the paper under review the authors classify automorphisms of finite order on compact connected simple Lie groups by which the induced Cartan embedding is an austere embedding. Furthermore, they consider the problem whether an austere Cartan embedding is weakly reflective or not.