A coordinate system composed of intersecting surfaces. If the intersections are all at right angles, then the curvilinear coordinates are said to form an orthogonal coordinate system. If not, they form a skew coordinate system. A general metric g_μν has a line element d s^2 = g_μν d u^μ d u^ν, where Einstein summation is being used. Orthogonal coordinates are defined as those with a diagonal metric so that g_μν congruent δ_ν^μ h_μ^2, where δ_ν^μ is the Kronecker delta and h_μ is a so-called scale factor.

curve | divergence | gradient | line element | metric | orthogonal coordinate system | scale factor | skew coordinate system