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The purpose of the present note is to show that the results recently announced by S. I. Goldberg (l) in this Bulletin are valid also in slightly more general forms. 1. Consider a conformai Killing vector vh in an ^-dimensional Rie- mannian space. Then the Lie derivative of the fundamental tensor gji and that of Christoffel symbols with respect to vh are respectively given by

Conformal transformations in Riemannian and Hermitian spaces