Like the dot product of the Gradient with a Vector field. The divergence measures the net flow of a field at a point, allowing to distinguish between field sources and sinks, and appears in many vector equations in physics, particularly Fluid mechanics, and Electromagnetism

Diveregence operator on Manifolds

Formal Adjoint to the Gradient operator on manifolds

See the Laplacian on a Riemannian Manifold: An Introduction toAnalysis on Manifolds