Arithmetic distance on compact symmetric spaces (Q1822367)

Using ''Helgason spheres'' (the minimal totally geodesic spheres in a compact irreducible symmetric space) the author defines an arithmetic distance for a compact irreducible symmetric space M and proves the following main Theorem. Let \(M=G_ p(K^ n)\), \(K={\mathbb{C}}\), H, or R, or \(M=AI(n)=SU(n)/SO(n)\), of rank greater than 1 and dimension greater than 3. Let L' be the geometric transformation group of M. Let \(L=\{\phi: M\to M: \phi\) be a diffeomorphism and \(\phi\) preserves arithmetic distance\(\}\). Then \(L=L'\).