INTEGRAIS COMPLEXAS DE ANCELMO L. GRACELI.

$f'(z)$ = [θ ${\frac {\sin t}{t}}.$ ] [θ ${\frac {\sin t}{t}}.$ ] Z COS π [θ ${\frac {\sin t}{t}}.$ ] [/] - Z SIN π [ ${\frac {\sin t}{t}}.$ ] d θ $\psi (z)$ =

$f'(z)$ = 1/ π $X$ $f'(z)$ Z COS π [θ ${\frac {\sin t}{t}}.$ ] [/] - Z SIN π [ ${\frac {\sin t}{t}}.$ ] d θ $\psi (z)$ =

INTEGRAIS COMPLEXAS DE ANCELMO LUIZ GRACELI

Z $\phi _{n}(x)$ = 1 / $\phi _{n}(x)$ { $\phi _{n}(x)$ Z COS ${\frac {\sin t}{t}}.$ [-] $\phi _{n}(x)$ Z SIN ${\frac {\sin t}{t}}.$ }=

INTEGRAIS COMPLEXAS DE ANCELMO LUIZ GRACELI

$f'(z)$ Z = 1 / ${\frac {\sin t}{t}}.$ { $\phi _{n}(x)$ Z COS $\phi _{n}(x)$ [-] $\phi _{n}(x)$ ${\frac {\sin t}{t}}.$ Z SIN $\phi _{n}(x)$ ${\frac {\sin t}{t}}.$ } d $\phi _{n}(x)$ =

INTEGRAIS COMPLEXAS DE ANCELMO LUIZ GRACELI

$f'(z)$ = Z = 1 / ${\frac {\sin t}{t}}.$ { $\phi _{n}(x)$ Z COS $\phi _{n}(x)$ [-] $\phi _{n}(x)$ ${\frac {\sin t}{t}}.$ Z SIN $\phi _{n}(x)$ } ${\frac {\sin t}{t}}.$ d θ=

INTEGRAIS COMPLEXAS DE ANCELMO LUIZ GRACELI

Z $\phi _{n}(x)$ = 1 / $\phi _{n}(x)$ { $\phi _{n}(x)$ Z COS $\phi _{n}(x)$ [-] $\phi _{n}(x)$ Z SIN $\phi _{n}(x)$ }=

INTEGRAIS COMPLEXAS DE ANCELMO LUIZ GRACELI

Z $\phi _{n}(x)$ = 1 / $\phi _{n}(x)$ { $\phi _{n}(x)$ Z COS $\phi _{n}(x)$ [-] $\phi _{n}(x)$ Z SIN $\phi _{n}(x)$ } D $\phi _{n}(x)$ =

INTEGRAIS COMPLEXAS DE ANCELMO LUIZ GRACELI

Z $\phi _{n}(x)$ = 1 / $\phi _{n}(x)$ { $\phi _{n}(x)$ Z COS $\phi _{n}(x)$ [-] $\phi _{n}(x)$ Z SIN $\phi _{n}(x)$ }π D θ=

x = θ, $X$ [ - COS θ, $X$ $\phi _{n}(x)$

y = -θ, $X$ COS θ, $X$ $\phi _{n}(x)$

Z = SIN $\phi _{n}(x)$

x = θ, $X$ π $\Psi$ [ - COS θ, $X$ π $\Psi$ ] COS u.

y = -θ, $X$ π $\Psi$ COS θ, $X$ π $\Psi$ ] SIN u

Z = SIN θ, $X$ π $\Psi$

$f'(z)$ x = θ, $X$ [ - COS θ, $X$ ] COS u. d θ, $X$

$f'(z)$ y = -θ, $X$ COS θ, $X$ ] SIN u d θ, $X$

Z = SIN θ, $X$

$f'(z)$ x = θ, $X$ π $\Psi$ [ - COS θ, $X$ π $\Psi$ ] COS u. d θ, $X$

$f'(z)$ y = -θ, $X$ π $\Psi$ COS θ, $X$ π $\Psi$ ] SIN u d θ, $X$

Z = SIN θ, $X$ π $\Psi$

$f'(z)$ x = θ, $X$ [ - COS θ, $X$ ] COS u.

$f'(z)$ y = -θ, $X$ COS θ, $X$ ] SIN u

Z = SIN θ, $X$

$f'(z)$ x = θ, $X$ π $\Psi$ [ - COS θ, $X$ π $\Psi$ ] COS u.

$f'(z)$ y = -θ, $X$ π $\Psi$ COS θ, $X$ π $\Psi$ ] SIN u

Z = SIN θ, $X$ π $\Psi$

$f'(z)$ $\phi _{n}(x)$

$f'(z)$ y = -θ, $X$ COS θ, $X$ ] SIN u d θ, $\phi _{n}(x)$

Z = SIN θ, $X$

$f'(z)$ x = θ, $X$ π $\Psi$ [ - COS θ, $X$ π $\Psi$ ] COS u. d θ, $X$

$f'(z)$ y = -θ, $X$ π $\Psi$ COS θ, $X$ π $\Psi$ ] SIN u d θ, $X$

Z = SIN θ, $\phi _{n}(x)$

INTEGRAIS COMPLEXAS DE ANCELMO LUIZ GRACELI.

$f'(z)$ = 2 $X$ $f'(z)$ COS Z π $\Psi$ θ - SIN Z π $\phi _{n}(x)$

$\Psi$ $f'(z)$ = $f'(z)$ = N / π $X$ $f'(z)$ COS Z π $\Psi$ θ - SIN Z π θ $\phi _{n}(x)$

INTEGRAIS COMPLEXAS DE ANCELMO LUIZ GRACELI

x = θ, $X$ [ - COS θ, $X$ ] COS u.

y = -θ, $X$ COS θ, $X$ ] SIN u

Z = SIN θ, $X$

x = θ, $X$ π $\Psi$ [ - COS θ, $X$ π $\Psi$ ] COS u.

y = -θ, $X$ π $\Psi$ COS θ, $X$ π $\Psi$ ] SIN u

Z = SIN θ, $X$ π $\Psi$

$f'(z)$ x = θ, $X$ [ - COS θ, $X$ ] COS u. d θ, $X$

$f'(z)$ y = -θ, $X$ COS θ, $X$ ] SIN u d θ, $X$

Z = SIN θ, $X$

$f'(z)$ x = θ, $X$ π $\Psi$ [ - COS θ, $X$ π $\Psi$ ] COS u. d θ, $X$

$f'(z)$ y = -θ, $X$ π $\Psi$ COS θ, $X$ π $\Psi$ ] SIN u d θ, $X$

Z = SIN θ, $X$ π $\Psi$

$f'(z)$ x = θ, $X$ [ - COS θ, $X$ ] COS u.

$f'(z)$ y = -θ, $X$ COS θ, $X$ ] SIN u

Z = SIN θ, $X$

$f'(z)$ x = θ, $X$ π $\Psi$ [ - COS θ, $X$ π $\Psi$ ] COS u.

$f'(z)$ y = -θ, $X$ π $\Psi$ COS θ, $X$ π $\Psi$ ] SIN u

Z = SIN θ, $X$ π $\Psi$

$f'(z)$ x = θ, $X$ [ - COS θ, $X$ ] COS u. d θ, $X$

$f'(z)$ y = -θ, $X$ COS θ, $X$ ] SIN u d θ, $X$

Z = SIN θ, $X$

$f'(z)$ x = θ, $X$ π $\Psi$ [ - COS θ, $X$ π $\Psi$ ] COS u. d θ, $X$

$f'(z)$ y = -θ, $X$ π $\Psi$ COS θ, $X$ π $\Psi$ ] SIN u d θ, $X$

Z = SIN θ, $X$ π $\Psi$

INTEGRAIS COMPLEXAS DE ANCELMO LUIZ GRACELI.

$f'(z)$ = 2 $X$ $f'(z)$ COS Z π $\Psi$ θ - SIN Z π $\Psi$ θ, $X$ d θ,T =

$f'(z)$ = $f'(z)$ = N / π $X$ $f'(z)$ COS Z π $\Psi$ θ - SIN Z π $\Psi$ θ, $X$ d θ,T =

$f'(z)$ = N / π $X$ $f'(z)$ COS Z π $\Psi$ θ - SIN Z π $\Psi$ θ, $X$ d θ,T =

$f'(z)$ = 1/ π $X$ $f'(z)$ Z COS π [ $\psi (z)$ ] - Z SIN π [ $\psi (z)$ ] d $\psi (z)$ =

$f'(z)$ = 1/ π $X$ $f'(z)$ Z COS π - Z SIN π d $\psi (z)$ =

$f'(z)$ = 1/ π $X$ $f'(z)$ Z COS π [ $\psi (z)$ ] θ,- Z SIN π [ $\psi (z)$ ] θ, d $\psi (z)$ =

$f'(z)$ = 1/ π $X$ $f'(z)$ Z COS π θ, - Z SIN π θ, d $\psi (z)$ =

$f'(z)$ = 1/ π $X$ $f'(z)$ Z COS π [ $\psi (z)$ ] $g_{t}$ - Z SIN π [ $\psi (z)$ ] $g_{t}$ d $\psi (z)$ =

$f'(z)$ = 1/ π $X$ $f'(z)$ Z COS π $\Psi$ $g_{t}$ - Z SIN π $\Psi$ $g_{t}$ d $\psi (z)$ =

$f'(z)$ = 1/ π $X$ $f'(z)$ Z COS π [ $\psi (z)$ ] θ, $g_{t}$ - Z SIN π [ $\psi (z)$ ] θ $g_{t}$ , d $\psi (z)$

$f'(z)$ = 1/ π $X$ $f'(z)$ Z COS π θ, $g_{t}$ - Z SIN π θ, $g_{t}$ d $\psi (z)$ =

variedade complexa. $X$

Fluxo de Ricci normalizado

Suponha que $M$ seja uma variedade suave compacta, e seja $g_{t}$ um fluxo de Ricci para $t$ no intervalo $(a,b)$ .

INTEGRAIS DE ANCELMO LUIZ GRACELI.