# Koszul connexion

1. Mar 3, 2015

### Calabi

Hell every body, do you know what is a Koszul connexion please? WIkipédia francais is not clear

I just know if I have a vectorial bundle $$\pi : E \rightarrow B$$, a vectorial field X on B and a section S on B. A connexion associate at those 2 object an other section.

But it's nt clear.

Thank you in advance and have a nice afternoon.

2. Mar 3, 2015

### lavinia

Did you read the English Wikipedia article? It is very clear.

http://en.wikipedia.org/wiki/Connection_(vector_bundle)

3. Mar 3, 2015

### Calabi

I prefere the french formulation(whitout the tensor for the moment.). than the english. But the french is not clear. On the french version what is f please?

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7. Mar 3, 2015

### lavinia

Calabi, f is a smooth function. X is a tangent vector at a point on the manifold. Note that s is a section of a vector bundle - but not necessarily the tangent bundle.

Can you ask some specific questions. I do no want to just repeat what the Wikipedia article is saying.

8. Mar 4, 2015

### Calabi

The thing is they don't specifise the definition set and the arrived set of f it's just what's stike me.
That's why I'm wooriing of. Excuse me if you you think I want you to repaet what wikipédia said.

9. Mar 4, 2015

### lavinia

Milles pardons Pour moi, l'article de Wikipedia est précis et sans des questions spécifiques je ne sais pas comment l'expilquer d'une autre manière. (Pardonnez mon mauvais français).

La fonction,f , est défini sur la base,la variété, meme comme le champs de vecteurs.

En general il n'existe pas une section globale d'un fibre vectoriel sans des zeros mais c'est toujours possible de l'éloigner a travers tout le variété en le faisant zero a l'extérieur d'un voisinage ouvert. En ce cas, on ne s'inquiet pas aux zeros mais seulement au voisinage non-zero.