The index of exceptional symmetric spaces

Jürgen Berndt; Carlos Olmos; Juan Sebastián Rodríguez

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arXiv · 1905.06250

The index of exceptional symmetric spaces

Jürgen Berndt·Carlos Olmos·Juan Sebastián Rodríguez

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Abstract

The index of a Riemannian symmetric space is the minimal codimension of a proper totally geodesic submanifold (Onishchik, 1980). There is a conjecture by the first two authors for how to calculate the index. In this paper we give an affirmative answer to this conjecture for the exceptional Riemannian symmetric spaces and for the classical symmetric spaces Sp(r,R)/U(r). Our methodology is new and based on the idea of using slice representations for studying totally geodesic submanifolds.

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Jürgen Berndt, Carlos Olmos, Juan Sebastián Rodríguez. 2019-05-15. The index of exceptional symmetric spaces. https://arxiv.org/abs/1905.06250

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