Abstract
For a given symmetric space of compact type, it is known that a certain Riemannian submersion of a Hilbert space onto the symmetric space is nat-urally defined. In this paper, we describe the principal curvatures and the principal distributions of the inverse image (which becomes a proper Fredholm submanifold) of a curvature adapted submanifold in the symmetric space under this Riemannian submer-sion. The curvature adapted submanifold is minimal if and only if the inverse image is formally minimal in certain sense.
