ON SOME SPACES OF MINIMAL GEODESICS IN RIEMANNIAN SYMMETRIC SPACES

Let (P, o) be a pointed irreducible symmetric space of compact type. In this paper, we study the space of minimal (i.e. shortest) geodesics in P from o to a point in the center of (P, o). More precisely, we first give a complete description of these geodesics. We then show that each connected component of the locus described by the midpoints of these geodesics is an extrinsically symmetric space (symmetric R-space) which is totally geodesically and isometrically embedded in P.