On weakly reflective submanifolds in compact isotropy irreducible Riemannian homogeneous spaces

Masahiro Morimoto

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arXiv · 2003.04674

On weakly reflective submanifolds in compact isotropy irreducible Riemannian homogeneous spaces

Masahiro Morimoto

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Abstract

We show that for any weakly reflective submanifold of a compact isotropy irreducible Riemannian homogeneous space its inverse image under the parallel transport map is an infinite dimensional weakly reflective PF submanifold of a Hilbert space. This is an extension of the author's previous result in the case of compact irreducible Riemannian symmetric spaces. We also give a characterization of so obtained weakly reflective PF submanifolds.

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Masahiro Morimoto. 2020-03-10. On weakly reflective submanifolds in compact isotropy irreducible Riemannian homogeneous spaces. https://arxiv.org/abs/2003.04674

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