Conformal vector field

A conformal vector field is like a special type of arrow that tells you how to change things in a certain way. Imagine you have a big, squishy balloon. If you stretch the balloon in one direction, it will get longer, but if you squash it in another direction, it will get shorter. A conformal vector field is like an arrow that tells you how to stretch or squash the balloon without changing its overall shape. It's kind of like a magic arrow that keeps everything the same, but makes it bigger or smaller in a special way. Scientists use conformal vector fields to study things that change in a very specific way, like fluids and the universe.