Usefulness of Differential Geometry I recently came across these books:

Differential Geometry and Lie Groups: A Computational Perspective
Differential Geometry and Lie Groups: A Second Course

Their subject matter really intrigues me, as I really enjoy topology/geometry/analysis, but had not planned to pursue them since I also want to work in an area with very concrete application. However, I am skeptical. At one point I thought topological data analysis (TDA) was the perfect marriage of my interests, but I have found very little evidence of that field actually being used in computer science, much less in industrial or otherwise more 'practical' settings. It seems like TDA makes mathematicians feel more relevant to the data science world, but I'm not convinced that it makes them so (feel free to contradict me if you think I'm wrong on this point, but note that I want a concrete use case, not an abstract argument about its relevance). I have similar stories about coding theory, certain aspects of set theory, etcetera. They may have theoretical relevance, but is there any situation where, in the process of developing software, one might need to consult theses fields? I don't know of any.
So now my question: is there any practical field of computer science that makes advanced use of differential geometry? Medical imaging, other imaging, computer graphics, virtual reality, and some other fields come to mind as potential application areas. In my (admittedly limited) experience, however, these areas seem to use basic 3D geometry, numerical linear algebra, and sometimes numerical analysis of PDEs. Those are all very nice topics, but they do not require anything as abstract as differential geometry.
Thanks in advance.
If you found Structure and Interpretation of Computer Programs interesting, you might like Functional Differential Geometry (It's from the same authors) .

Differential geometry is deceptively simple. It is surprisingly easy to get the right answer with unclear and informal symbol manipulation.  To address this problem we use computer programs to communicate a precise understanding of the computations in differential geometry.  Expressing the methods of differential geometry in a computer language forces them to be unambiguous and computationally effective. The task of formulating a method as a computer-executable program and debugging that program is a powerful exercise in the learning process.  Also, once formalized procedurally, a mathematical idea becomes a tool that can be used directly to compute results.

Taken from Sussman, Wisdom: Functional Differential Geometry