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searching for Harmonic differential 5 found (6 total)

Hodge theory (4,288 words) [view diff] no match in snippet view article find links to article

In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential

Cauchy–Riemann equations (4,675 words) [view diff] exact match in snippet view article find links to article

vdx+udy{\displaystyle v\,dx+u\,dy} is both closed and coclosed (a harmonic differential form). Another formulation of the Cauchy–Riemann equations involves

Yang–Mills equations (3,691 words) [view diff] exact match in snippet view article find links to article

Yang–Mills connections can be seen as a non-linear analogue of harmonic differential forms, which satisfy d ω = d ∗ ω = 0 {\displaystyle d\omega =d^{*}\omega

Ddbar lemma (2,984 words) [view diff] exact match in snippet view article find links to article

_{\bar {\partial }}} . To these operators one can define spaces of harmonic differential forms given by the kernels: H d k = ker ⁡ Δ d : Ω k ( X ) → Ω k

Kähler identities (3,994 words) [view diff] exact match in snippet view article find links to article

inequalities are a pair of inequalities associated to inner products of harmonic differential forms with the curvature of a Chern connection on a holomorphic