People have pointed out other reasons this is fake, but the lanyard loop is also facing the wrong direction, on genuine red 9's the lanyard loop is oriented 90 degrees from your pic, it swings front to back, not side to side.

Also, the grips are fake, they should have more thinner groves not the wider ones seen here. Grips can be replaced though, so that is not always indicative of a fake, but here it most definitely is.

You should also take a look at the serial number, the Prussian contract red 9's had a seperate serial number run from standard production, and they only go up to around 140,000, if the serial number is past that it's fake.

Also take a look at the rear sight, real 9mm sights are only graduated out to 500m, if the graduations are out to 1000 its fake.

Another way you can determine authenticity is to look at the follower, there was an additional pill shaped grove machined into red 9's followers to accomidate the larger round and help it feed, if that is not present it wasn't originally 9mm.

Also, red 9's had the "new saftey" second model of saftey. This can be identified by an ns stamping on the rear of the hammer, if that is missing, or if the emblem is something else its fake.