A formula for the radial part of the Laplace-Beltrami operator
Sigurđur Helgason · Journal of Differential Geometry · 1972
Let V be a manifold and H a Lie transformation group of V. Suppose Du = 0 is a differential equation on V, both the differential operator D and the function u assumed invariant under H. Then the differential equation will involve several inessential variables, a fact which may render general results about differential operators rather ineffective for the differential equation at hand. Thus although D may not be an elliptic operator it might become one after the inessential variables are eliminated (cf. [3, p. 99]).