codifferential

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English[edit]

Etymology[edit]

co- +‎ differential

Noun[edit]

codifferential (plural codifferentials)

  1. (mathematics) The projected differential of an extensor field.
    • 2016, Terence Tao, “Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation”, in arXiv[1]:
      In the language of differential geometry, the incompressible inviscid Euler equations can be written in vorticity-vector potential form as where is the vorticity -form, denotes the Lie derivative with respect to the velocity field , is the Hodge Laplacian, is the codifferential (the negative of the divergence operator), and is the canonical map from -forms to -vector fields induced by the Euclidean metric .
  2. (differential geometry) the formal adjoint of the exterior derivative; a differential-geometric version of the divergence operator; the exterior derivative sandwiched between two Hodge star operators with some additional factor(s) that take(s) care of the sign; the Hermitian conjugate of the exterior derivative under the inner product for k-form fields over some manifold M: , so that .
    • 2015, 2 Tangent Space, Differential Forms, Metric (Mathematics for Theoretical Physicists - Hirosi Ooguri)‎[2], K Raviteja (YouTube), spoken by Hiroshi Ooguri (Hiroshi Ooguri), 1:19:34 from the start:
      One important concept is the introduction of codifferential operator

Further reading[edit]