Measure-preserving mappings from the unit cube to some symmetric spaces

Abstract

We construct measure-preserving mappings from the d-dimensional unit cube to the d-dimensional unit ball and the compact rank one symmetric spaces, namely the d-dimensional sphere, the real, complex, and quaternionic projective spaces, and the Cayley plane. We also give a procedure to generate measure-preserving mappings from the d-dimensional unit cube to product spaces and fiber bundles under certain conditions.