On Weakly Reflective Submanifolds in Compact Isotropy Irreducible Riemannian Homogeneous Spaces

Masahiro Morimoto, H. Izeki

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)467-476
Number of pages10
JournalTokyo Journal of Mathematics
Volume44
Issue number2
DOIs
Publication statusPublished - 2021 Dec

Keywords

  • Isotropy irreducible
  • Minimal submanifold
  • PF submanifolds in Hilbert spaces
  • Weakly reflective submanifold

ASJC Scopus subject areas

  • Mathematics(all)

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