Holomorphic Isometries from the Unit Ball into Symmetric Domains

We construct rational isometric holomorphic embeddings of the unit ball into higher rank symmetric domains D, first discovered by Mok, in an explicit way using Jordan triple systems, and we classify all isometric embeddings into tube domains of rank 2. For symmetric domains of arbitrary rank, including the exceptional domains of dimension 16 and 27, respectively, we characterize the Mok type mapping in terms of a vanishing condition on the second fundamental form of the image of F in D.