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}