Tangential Cauchy–Riemann equations

Summary

The tangential Cauchy–Riemann equations on a real submanifold of $\C^n$ are a restricted form of the Cauchy–Riemann equations, see the definition. They are taken only in the anti-holomorphic directions that are tangent to the submanifold. Their solutions are the CR functions, and every restriction of a holomorphic function is one. They form an overdetermined system of first-order linear partial differential equations. Hans Lewy's study of them led to his example of a linear equation with no solutions.