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.
- Isotropy irreducible
- Minimal submanifold
- PF submanifolds in Hilbert spaces
- Weakly reflective submanifold
ASJC Scopus subject areas
- General Mathematics