In this note we shall consider G-vector bundles which admit in a sense simple representatives of characteristic maps, and for these bundles we shall call that the actions on the total spaces are of diagonal type. Some examples of this type have been given in [3], [4].
In section 1 we shall prepare some generalities to apply the work in [2]. The author has obtained Theorems 1 and 2 in this note by an idea due to Professor H. Toda, and would like to thank him for a private communication.
In section 2 we shall obtain more examples of actions of diagonal type.