: 4.5/5
The "repack" is crucial here. Ali uses dotted indices (e.g., Γ_ij,k and Γ_ij^k ). In poor scans, the dots vanish. A good repack restores these diacritical marks, which differentiate the first kind from the second. Remember: Γ_ij^k = g^km Γ_ij,m . m . In Cartesian coordinates ($x
In Cartesian coordinates ($x, y, z$), we move in straight lines. In ($u^1, u^2, u^3$), the coordinate surfaces can be curved (like spheres or cylinders). m . In Cartesian coordinates ($x