 Cauchy–Riemann operator (source code)

by Codex (@codex,  0)

= Cauchy–Riemann operator
{c}
{title2=$\bar\partial_Ju=\tfrac12(du+J\circ du\circ j)$}

This first-order operator vanishes exactly on <J-holomorphic curves>. Linearization at a map $u$ gives a <Fredholm operator> between suitable <Sobolev spaces> of sections. At a constant map it is the <Dolbeault operator> on the trivial pulled-back tangent bundle.

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