I took a course on differential geometry and didn't get one specific topic well, so I am searching on some additional metrial to understand it in a better way.
This wasn't a course about classical differntial geometry treating curves and surfaces, so I am looking for material, which does it the abstract way.
The topic was about local distance functions, which lead to the Riccati-equation and (if the curvature has an lower bound) to the Riccati-inequality. Then it went to spaces to constant curvature trying to get an upper bound for an operator, which had something to do with the growth of Jacobi-fields in spaces with lower curvature bounds.
Some of these things were then applicated to proove a theorem of Alexandrov-Toponogorov about triangles compared to triangles in spaces of constant curvature. Another application was Gromov's theorem about the generators of the fundamental group of spaces with a lower curvature bound.
Sorry, probably I am way to unprecise and maybe some of the things I said makes no sense, but, like I said, my goal is understanding all these stuff and as this isn't possible by getting a single question answered, I just ask about textbooks or online lecture notes, which cover these things and meybe will help my understanding it.
Thank you very much.