MHB What are the practical applications of differential geometry?

[mathmari]

Hey!

In what jobs is differential geometry applied and needed?

 

[Ackbach]

Well, I'm not sure I can fully answer your question. But here is a link to the applications page for differential geometry on the wiki. Then you could figure out which jobs apply the academic fields there mentioned.

 

[ThePerfectHacker]

I am not sure, but I would not be surprised if DG is not used anywhere outside of math and physics. Even something as basic calculus is not used by engineers on problems they work with. It is true that there are problems from engineering that need calculus to solve them, but engineers do not need to do it. It has either been solved by previous engineers, who written it down in a manual, or with today's technology it is stored or solved through a computer. I asked engineers who do real engineering work and they all told me they do not really require math. Therefore, if I have to guess I would say that DG is the same.

 

[Deveno]

If you want to improve on three-dimensional modelling of physical systems (such as that used by the Havok physics engine in many popular current video games), differential geometry is going to be *very* useful. As with other applications, it's a niche market. This is the way of the modern world, very few skills have applications to all walks of life.

Of course, once created, such an application can often be used by the end-user with little or no training in the skills used to make it (by analogy, one does not need to be a machinist or automotive engineer in order to drive a car).

Many scientific and mathematical concepts are like this: only truly useful (in the sense of getting paid for knowing them) in small specialized settings. Of course, teaching others being the "obvious" application.