Timer3 Complementary output

Hi guys,

I have a programming problem:
I need a complementary PWM signal with exactly the same frequency.
I just initialized the second PWM output later, but unfortunately that does not work the way I want it. The oszi does not indicate a phase shift.

#include "TimerThree.h"
#include "TimerOne.h"
#include <LiquidCrystal.h>


LiquidCrystal lcd(8, 9, 4, 5, 6, 7);      //Definiert die Pins fuer das LCD-Display

int PWMAusgang1 = 2;  //2,3 oder 5
int PWMAusgang2 = 3;  //2,3 oder 5
double Frequenz = 47000;
long Periodendauer =  (1 / Frequenz * 1000000);
double tastverhaeltnis = 50;
double einschaltzeit;

void setup() {

  
  einschaltzeit = (tastverhaeltnis / 100 * 1024);
  int verzoegerung = (int)((100-tastverhaeltnis)*Periodendauer);
  

  pinMode(PWMAusgang1, OUTPUT);                 //Definiere Pins als Output
  pinMode(PWMAusgang2, OUTPUT);
  Timer3.initialize(Periodendauer);             //Inizialisiere Timer mit Periodendauer

  Timer3.pwm(PWMAusgang1, einschaltzeit);
  delay(verzoegerung);
  Timer3.pwm(PWMAusgang2, einschaltzeit);

}

Does anybody has an idea how to fix it?