codifferentials

Noun

codifferential (plural codifferentials)

1. The projected differential of an extensor field.
   • In the language of differential geometry, the incompressible inviscid Euler equations can be written in vorticity-vector potential form as #92;begin#123;matrix#125;#92;partial#95;t#92;omega#43;#123;#92;mathcalL#125;#95;u#92;omegaamp;#61;0#92;#92;uamp;#61;#92;delta#92;tilde#92;eta#123;-1#125;#92;Delt...2016, Terence Tao, “Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation”, in arXiv
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: (α,β)=∫_Mα∧⋆β, so that (α,dβ)=(δα,β).
   • One important concept is the introduction of codifferential operator2015, 1:19:34 from the start, in 2 Tangent Space, Differential Forms, Metric (Mathematics for Theoretical Physicists - Hirosi Ooguri), spoken by Hiroshi Ooguri (Hiroshi Ooguri), K Raviteja (YouTube)