File:Affine connection example.svg
Summary
| Description |
English: The metric is ds2 = dr2 + dθ2. The red vector field Y sends dθ to r, and the blue vector field X sends dr to 1. Thus ∇YX=0. The red vector field in |
| Date | |
| Source | Own work |
| Author | IkamusumeFan |
| Other versions |
 |
| SVG development | Category:Valid SVG created with Gnuplot code#Affine%20connection%20example.svg  This plot uses embedded text/digits. |
| Source code | Gnuplot code# Author: Ika
# Date: 12/31/2014
set term svg font 'Times, 18' size 1000,1000
set output 'affine_conn_eg.svg'
set size ratio 1
set xrange [-1.5:1.5]
set yrange [-1.5:1.5]
# Unit along the axes
set xtics 1
set ytics 1
unset grid
unset label
set key off
# The following block shows the red vector field.
# j stands for a different radius r
do for [j=1:25] {
r = 2/25.0*j
# i stands for a different angle \theta
do for [i=1:50] {
theta = 2*pi/50.0*(i-1)
set arrow j*50+i from r*cos(theta), r*sin(theta) to r*(cos(theta)-0.5*sin(theta)), r*(sin(theta)+0.5*cos(theta)) lw 1 lc rgb "red"
}
}
# The following block shows the blue vector field.
# j stands for a different radius r
do for [j=1:10] {
r = 2/10.0*j
# i stands for a different angle \theta
do for [i=1:50] {
theta = 2*pi/50.0*(i-1)
set arrow j*50+i+2000 from r*cos(theta), r*sin(theta) to (r+0.1)*cos(theta), (r+0.1)*sin(theta) lw 1 lc rgb "blue"
}
}
# To show the arrows, I have to plot something. So I choose a trivial zero function.
set parametric
plot 0,0 lw 1 lc rgb "rgb"
set term x11
set output
|
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
