latex-pictures
A collection of TikZ drawings and other images 🖌️
smooth-function.tikz (1410B)
1 % This picture represents the definition of a smooth map between manifolds 2 % Copyright Pablo (C) 2021 3 \begin{tikzpicture} 4 % The manifolds 5 \begin{scope}[shift={(-2, 0)}] 6 \draw (-1.5, -0.5) to[relative, out=20, in=160] 7 +( 2, 0) to[relative, out=20, in=160] 8 +( 1, 1) to[relative, out=-20, in=-160] 9 +( -2, 0) to[relative, out=-20, in=-160] 10 cycle; 11 \draw (0.5, -0.5) node[right]{$M$}; 12 \end{scope} 13 \begin{scope}[shift={(2, 0)}] 14 \draw (-1.5, -0.5) to[relative, out=20, in=160] 15 +( 2, 0) to[relative, out=20, in=160] 16 +( 1, 1) to[relative, out=-20, in=-160] 17 +( -2, 0) to[relative, out=-20, in=-160] 18 cycle; 19 \draw (0.5, -0.5) node[right]{$N$}; 20 \end{scope} 21 22 % The functions 23 \draw[->] (-1, 0.9) to[out=30, in=150] node[above]{$f$} (1, 0.9); 24 \draw[->] (-1, -1.7) to[out=30, in=150] 25 node[above]{$\psi \circ f \circ \varphi^{-1}$} (1, -1.7); 26 \draw[->] (-2, -0.7) -- node[left]{$\varphi$} +(0, -1); 27 \draw[->] ( 2, -0.7) -- node[left]{$\psi$} +(0, -1); 28 29 % The open sets in euclidian space 30 \draw[dashed] (-2, -3) node{$\varphi(U)$} ellipse (1 and 0.5); 31 \draw[dashed] ( 2, -3) node{$\psi(V)$} ellipse (1 and 0.5); 32 \draw (-3.5, -4) node[left]{$\mathbb{R}^m$} rectangle +(3, 2); 33 \draw ( 0.5, -4) node[left]{$\mathbb{R}^n$} rectangle +(3, 2); 34 \end{tikzpicture}