The codifferential δ of a k-form on an n-dimensional Riemannian manifoldMathworldPlanetmath is given by:


where is the Hodge star operator and d is the exterior derivativeMathworldPlanetmath.

Let g denote the matrix locally representing the metric with respect to co-ordinates x1,,xn. Then for a 1-form w we have:

Title codifferential
Canonical name Codifferential
Date of creation 2013-03-22 18:37:11
Last modified on 2013-03-22 18:37:11
Owner whm22 (2009)
Last modified by whm22 (2009)
Numerical id 5
Author whm22 (2009)
Entry type Definition
Classification msc 53B21
Related topic DifferentialForms
Related topic Laplacian