Do not skip the solved problems. Differential geometry requires a strong grasp of vector calculus algebraic manipulation. Working through the solved examples will teach you the "tricks" of simplifying complex determinants and vector products.
The straightest possible paths on a curved surface (the generalization of straight lines to curved spaces), governed by the geodesic differential equations. differential geometry krishna publication pdf
To get the most out of your study sessions, consider the following strategy: Do not skip the solved problems
: Clear mathematical derivations for geodesics, mapping, and the Gauss-Bonnet theorem. Tensor Calculus Integration differential geometry krishna publication pdf