Good applied differential geometry books I'm searching a book which goes about how Differential Geometry can be applied to solve Real world problems. I tried William L Burke's book, but I found it to be all over the place. The information, at least in the first chapter, seemed to have no continuity. A book that I liked is Tristan Needham's Visual Differential Geometry, and while it only goes indirectly over the matter, I liked Penrose's Road to reality as well.
 A: Personally I like differential geometry a lot and also like to find more about their applications. Not sure if there is an overview book talking about all the applications, but for each field there are a few books that were trying to apply the tools of DiffGeom.
In physics, I feel the whole field of General relativity is a huge application of differential geometry...If that count then any good GR textbook shall show many applications. The one I like a lot is Sean Carroll's Spacetime and Geometry.
Control theory and dynamic systems also had some applications of differential geometry, esp. the domain of operation is no longer euclidean spaces but manifolds. One I knew is : Geometric control theory
For statistics, there is a specific domain called Information Geometry, applying tools from DiffGeom to the space of distributions and analyzing their metric structure. This line of research give rise to the algorithm natural gradient descent etc in optimization.
In machine learning, DiffGeometry has been used to analyze generative models (If you search "Geometry deep generative model" on google scholar you can get a few. I had a paper along this direction.
