Differential operators | Differential geometry
Invariant differential operator
In mathematics and theoretical physics, an invariant differential operator is a kind of mathematical map from some objects to an object of similar type. These objects are typically functions on , functions on a manifold, vector valued functions, vector fields, or, more generally, sections of a vector bundle. In an invariant differential operator , the term differential operator indicates that the value of the map depends only on and the derivatives of in . The word invariant indicates that the operator contains some symmetry. This means that there is a group with a group action on the functions (or other objects in question) and this action is preserved by the operator: Usually, the action of the group has the meaning of a change of coordinates (change of observer) and the invariance means that the operator has the same expression in all admissible coordinates. (Wikipedia).
