Normally, swans will chase the geese, not vice versa, but there is always the exception. Are the geese wild or captive? This behavior may be due to the nesting season. If the geese are captive (not wild), you need to capture them and place them in a nesting pen until their hormone levels settle. This will also allow the swan to become more confident and learn to re-take his habitat and defend it.

If they are wild geese, you need to try and dissuade them from coming into the habitat, noise, chasing, not feeding, etc., may help this situation. Is there a way to fence the pond (top to bottom so that predators/geese cannot access your swan?

Do you know how the female died? Predator, etc? If so, this might be why the male is so frightened. Also, are you absolutely sure that it was the female that was killed? If it was the male, then this would also explain the behavior because the female would be a little more wary of her habitat without a male (her mate/protector). The Regal Swan