I want to draw a curved line and put a tensor above and below a node on it, something like this:

I tried this:
\documentclass{scrartcl}
\usepackage{tensor}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=0.8]
\draw[line width=4pt] (0,0) ..controls (2,2) and (5,-1) .. (10,2);
node[pos=0.5,below right, inner xsep=-1ex] {$\tensor{g}{_a_b}$}
\end{tikzpicture}
\end{document}
I know that I'm mixing it up with something else, but I do not enough time. Thanks!

inner septhat is larger (0.333em), so the node will be larger than4ptanyway. In the updated code I set the inner sep to zero, making this more predictable. – Torbjørn T. Oct 08 '15 at 21:49