A tensor above a node on a curved line on a gradient background

Question

In my last question, here, I asked how to draw a curved line with a tensor below a node on it. Now I would like to draw a more complicated figure with tikz: a curved line with nodes and tensors on it that lie on a gradient background. Something like this: Thanks for your help!

Answer 1

One option:

The code:

\documentclass[border=5pt]{standalone}
\usepackage{tensor}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
\filldraw[left color=gray!30,right color=black!60]
  (-2,-3) to[out=20,in=160]
  (11,-2) to[out=110,in=230]
  (13,4) to[out=180,in=20]
  (-1,3) to[out=220,in=130]
  cycle; 
\draw[line width=2pt] 
  (0,0) ..controls (2,2) and (5,-1) .. (10,2)
    node[fill,circle,minimum size=8pt,inner sep=0pt,pos=0.4,label=below:{$\tensor{g}{_a_b}$},label=above:{$t=0$}] {}
    node[fill,circle,minimum size=8pt,inner sep=0pt,pos=0.8,label=below:{$\tensor{g}{_a_b}$},label=above:{$t$}] {};
\node at (10,-1) {$\tensor{h}{_a_b}$};
\end{tikzpicture}

\end{document}