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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: enter image description here

Rodrigo de Azevedo
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harlekin
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  • "fibration into spheres of" should be "sphere bundle of". That's all I can say given the information you provided... – Bruno Joyal Sep 28 '13 at 17:50
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    It would probably help to have the name of the article, and, if possible, a scan of the portion you are having difficulty translating. – user642796 Sep 28 '13 at 17:54
  • The natural fibration $G/K$->$G/H$ is therefore, $ \textbf{in this case} $, the fibration into spheres of a vector bundle over $G/H$ with structure group $H$...$G$-invariant – wwbb90 Sep 28 '13 at 18:05
  • @ArthurFischer I have added a scan of the section and I also added the title to the post. – harlekin Sep 28 '13 at 18:10
  • @harlekin: Thanks. This will make it easier if someone has access to a (possibly better) copy of the same paper, or if there are contextual issues with the translation that are easier resolved having access to some more information about the paper itself. – user642796 Sep 28 '13 at 18:36

1 Answers1

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I think it means the following.

The natural fibration $G/K \to G/H$ is therefore the sphere bundle associated to a vector bundle over $G/H$ (I think he means the unit sphere bundle associated to a vector bundle with an inner product, but I don't have access to the paper), with structure group $H$, which is $G$-invariant.

I am fluent in French, so I tried to translate the meaning as much as I could, except that, as you say, some words are not clear in your copy.

Malkoun
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