Tohoku Mathematical Journal
2019
September
SECOND SERIES VOL. 71, NO. 3

Tohoku Math. J.
71 (2019), 397-424

Title EXAMPLES OF AUSTERE ORBITS OF THE ISOTROPY REPRESENTATIONS FOR SEMISIMPLE PSEUDO-RIEMANNIAN SYMMETRIC SPACES

Author Kurando Baba

(Received November 24, 2015, revised June 13, 2017)
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.

Mathematics Subject Classification. Primary 53C40; Secondary 53C35.
Key words and phrases. Austere submanifold, pseudo-Riemannian symmetric space, s-representation, restricted root system.

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