There are many things that are called "curvature". For example, Menger's curvature which plays an important role in Anaysis. Search "Menger curvature" anywhere in Mathscinet, to find out what is this.

I suppose that Levi-Chivita was the first to use connections, however I think that the term was introduced by E. Cartan.

There are many things that are called "curvature". For example, Menger's curvature which plays an important role in Anaysis. Search "Menger curvature" anywhere in Mathscinet, to find out what is this.

I suppose that Levi-Civita was the first to use connections, however I think that the term was introduced by E. Cartan.