We study families of submanifolds in symmetric spaces of compact type arising as exponential images of -orbits of variable radii. If the -orbit is symmetric such submanifolds are the most important examples of adapted submanifolds, i.e. of submanifolds of symmetric spaces with curvature invariant tangent and normal spaces.
Peter QUAST. "`Spindles' in symmetric spaces." J. Math. Soc. Japan 58 (4) 985 - 994, October, 2006. https://doi.org/10.2969/jmsj/1179759533