Hermitian spaces in geodesic correspondence

Abstract

1. Coburn [1] has studied the problem of Hermitian spaces in geodesic correspondence. He found a necessary and sufficient condition for two Kahler spaces to be in geodesic correspondence and showed that such correspondence was impossible between a Kahler space and a Hermitian space. The problem of geodesic correspondence between two Hermitian spaces he left unsolved. It will be shown that Coburn's first result is incorrect, as was pointed out by Bochner [2 ]; and we shall solve the general problem, giving necessary and sufficient conditions for two Hermitian spaces to be in geodesic correspondence.