latex-pictures

 % This picture represents the definition of a smooth manifold
 % Copyright Pablo (C) 2021
 \begin{tikzpicture}
   % The manifold
   \begin{scope}[shift={(-0.5, 0)}]
     % The frontire
     \draw (-4, 2) to[relative, out=20, in=160] 
           ( 2, 0) to[relative, out=20, in=160] 
           ( 4, 3) to[relative, out=-20, in=-160] 
           cycle;
     \draw (-4, 2) node[below]{$M$};
 
     % The open sets of the manifold and their intersection
     \begin{scope}[shift={(1, 2.2)}]
       \draw (-0.5, 0) ellipse (0.7 and 0.5);
       \draw (-1.2, 0) node[right]{$U$};
       \draw (0.5, 0) ellipse (0.7 and 0.5);
       \draw (1.2, 0) node[left]{$V$};
       \clip (-0.5, 0) ellipse (0.7 and 0.5);
       \draw[pattern=north west lines] (0.5, 0) ellipse (0.7 and 0.5);
     \end{scope}
   \end{scope}
 
   % The cards
   \draw[->] (-0.7, 1.7) to[relative, out=-20, in=-160] 
             node[left]{$\varphi_U$} (-2, -0.7);
   \draw[->] (1.7, 1.7) to[relative, out=20, in=160] 
             node[right]{$\varphi_V$} (2, -0.7);
 
   % The corresponding open sets in euclidian space
   \begin{scope}[shift={(0, -1.5)}]
     % The open sets
     \draw (-2, 0) ellipse (1 and 0.6) (2, 0) ellipse (1 and 0.6);
     \draw (-3, 0.5) node[above]{$\varphi_U(U)$};
     \draw (3, 0.5) node[above]{$\varphi_V(V)$};
 
     % The intersections
     \begin{scope}
       \clip (-2, 0) ellipse (1 and 0.6);
       \draw[pattern=north west lines] (-0.5, 0) ellipse (1 and 0.6);
     \end{scope}
     \begin{scope}
       \clip (2, 0) ellipse (1 and 0.6);
       \draw[pattern=north west lines] (0.5, 0) ellipse (1 and 0.6);
     \end{scope}
 
     % The diffeomorphism
     \draw[->] (-0.9, 0) -- 
               node[above]{$\varphi_V \circ \varphi_U^{-1}$} (0.9, 0);
   \end{scope}
 \end{tikzpicture}