紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2024, 61(4), p. 529-558

ORBITS OF THE ISOTROPY GROUP ACTION ON QUATERNIONIC SYMMETRIC SPACES

Sasaki, Yuuki

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2024-10

We investigate some geometric properties of orbits of the isotropy group action on quaternionic irreducible symmetric spaces of compact type. We show that such orbits, except for a one-point set, satisfy one of some four properties and classify which orbits satisfy which properties in each such symmetric space. In a symmetric space, a connected component of the fixed point set of a geodesic symmetry, except for a one-point set, is called a polar. A polar is a totally geodesic submanifold and an orbit of the isotropy group action. By the classification, we show that an orbit which is a quaternionic submanifold or the image of a totally complex immersion is a polar, and a polar becomes a quaternionic submanifold or the image of a totally complex immersion.

10.18910/98467

98467

ORBITS OF THE ISOTROPY GROUP ACTION ON QUATERNIONIC SYMMETRIC SPACES

Sasaki, Yuuki

Osaka University and Osaka City University, Departments of Mathematics

英語

2024-10

Osaka Journal of Mathematics

61

4

529

558

https://hdl.handle.net/11094/98467

10.18910/98467

https://doi.org/10.18910/98467