information:extraction, stylistic:style_transfer, quality:correction
Angles in Riemannian geometry

In Riemannian geometry, the metric tensor is used to define the angle between two tangents. Where U and V are tangent vectors and g are the components of the metric tensor G,

cos θ = g i j U i V j | g i j U i U j | | g i j V i V j |. {\displaystyle \cos \theta ={\frac {g_{ij}U^{i}V^{j}}{\sqrt {\left|g_{ij}U^{i}U^{j}\right|\left|g_{ij}V^{i}V^{j}\right|}}}.}