In this paper, for a compact symmetric space $M$ we consider orbits of the linear isotropy action of $M$ and the canonical action on $M$ of its isotropy group. We reduce some geometric conditions of these orbits to those of their starting points. Consequently we get some relations among the geometric conditions of orbits.
"Orbits of Isotropy Groups of Compact Symmetric Spaces." Tokyo J. Math. 24 (2) 407 - 428, December 2001. https://doi.org/10.3836/tjm/1255958184