See this sage-support link, where https://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/curve.html and https://sagemanifolds.obspm.fr/gallery.html are mentioned. We should add some of the most relevant of these pictures (or additional ones) to an observable place in the plot documentation - probably both the regular plot doc and as a note (and/or link to the appropriate place in manifolds) in the plot_slope_field and plot_vector_field places, both 2d and 3d.
CC: @egourgoulhon
Component: graphics
Issue created by migration from https://trac.sagemath.org/ticket/33711