Men can not compete in neither the World Championship nor the Olympics in synchronized Swimming.
I can see no reason for this at all. But the times are changing. Ironically in the early years Water Ballet was a men only sport. But the times are changing, today there are international competitions for men and also local competitions in several countries.
Unfortunately it seems that most of the men who train and compete in synchronized swimming are middle aged and slightly over weight. I seems lika most of them are doing this more as a political statement tan because they love the sport. There is also a swedish comedy about a group of men who train synchronized swimming called ”allt flyter” (Everything floats).