codifferential

Noun

Meaning

(mathematics) The projected differential of an extensor field.

(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
)
=

∫

M


α
∧
⋆
β


{\displaystyle (\alpha,\beta )=\int _{M}\alpha \wedge \star \beta }

, so that



(
α
,
d
β
)
=
(
δ
α
,
β
)


{\displaystyle (\alpha,d\beta )=(\delta \alpha,\beta )}

.

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