Let f be a complex-valued C 1 function defined in the neighborhood of a point z 0 . There are several notions closely related to conformality at z 0 . We say that f is isogonal at z 0 if whenever γ(t)...

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Let f be a complex-valued C1
function defined in the neighborhood of a point z0. There are several notions closely related to conformality at z0. We say that f is isogonal at z0
if whenever γ(t) and η(t) are two smooth curves with γ(0) = η(0) = z0, that make an angle θ there (|θ|
0, that is, if the limit


exists, is non-zero, and independent of θ.


Then f is isogonal at z0
if and only if it is isotropic at z0; moreover, f is isogonal at z0 if and only if either
’ (z0) exists and is non-zero, or the same holds for f replaced by
.




Answered Same DayDec 25, 2021

Answer To: Let f be a complex-valued C 1 function defined in the neighborhood of a point z 0 . There are...

Robert answered on Dec 25 2021
122 Votes
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