Tohoku Mathematical Journal

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

Kurando Baba

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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.

Article information

Source
Tohoku Math. J. (2), Volume 71, Number 3 (2019), 397-424.

Dates
First available in Project Euclid: 18 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1568772178

Digital Object Identifier
doi:10.2748/tmj/1568772178

Mathematical Reviews number (MathSciNet)
MR4012355

Subjects
Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 53C35: Symmetric spaces [See also 32M15, 57T15]

Keywords
austere submanifold pseudo-Riemannian symmetric space s-representation restricted root system

Citation

Baba, Kurando. Examples of austere orbits of the isotropy representations for semisimple pseudo-Riemannian symmetric spaces. Tohoku Math. J. (2) 71 (2019), no. 3, 397--424. doi:10.2748/tmj/1568772178. https://projecteuclid.org/euclid.tmj/1568772178


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