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Harmonic differential : ウィキペディア英語版 | Harmonic differential In mathematics, a real differential one-form ω on a surface is called a harmonic differential if ω and its conjugate one-form, written as ω *, are both closed. == Explanation ==
Consider the case of real one-forms defined on a two dimensional real manifold. Moreover, consider real one-forms which are the real parts of complex differentials. Let ω = ''A'' d''x'' + ''B'' d''y'', and formally define the conjugate one-form to be ω * = ''A'' d''y'' − ''B'' d''x''.
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