When a quotient is taken of a Riemannian manifold (or metric space in general), care must be taken to ensure that the quotient space is endowed with a metric that is well-defined. For instance, if a group G acts on a Riemannian manifold (X, g), then in order for the orbit space X / G to possess an induced metric, g must be constant along G -orbits in the sense that for any element h ∈ G and pair of vector fields X , Y we must have g (Xh, Yh) = g (X, Y).