Consider that I have a piece of paper, and I do a drawing on such paper. Now, consider the set of all possible "transformations" I can apply to this piece of paper that do not tear it. For example, I can rotate it, I can do an origami, I can make it into a cylinder... Is there a name for the set of all of such transformations?
Could I say that all these transformations are within the conformal transformations, i.e. since conformal transformations also have scaling, could I say that the set of such transformations that do not tear the paper are within the set of conformal transformations?