I am currently studying the following paper on Einstein manifolds:
L. Bérard Bergery, Sur de nouvelles variétés riemanniennes d'Einstein, Inst. Elie Cartan, Univ. Nancy №6, 1-60 (1983).
I have doubts that my translation of the following sentence is correct. Also the quality of my copy is poor unfortunately, at two points I have to guess the wording and this is particularly difficult since I don't speak French.
Here we go:
La fibration naturelle $G/K \to G/H$ est donc ici le fibré en sphère d'un fibré vectoriel sur $G/H$, de groupe structural H..(letters missing) G-invariant.
My translation:
The natural fibration $G/K \to G/H$ is therefore the fibration into spheres of a vector bundle over $G/H$, with structure group $H$ which is $G$-invariant.
In case this is difficult to judge I can provide more context.
Below is an image of the page in question:
