If you aren't able to solve the problem from the outside by convincing the building management to redirect the water somehow, you can at least try to solve the problem from the inside by adding mass to the glass roof.

Adding mass to the panels by applying a window tinting film to the glass panels or a vinyl film to the aluminum support beams should at least help to dampen the noise and lower the frequency (by which I mean the pitch, not the number of drips per minute) of the sound.

There are films designed to prevent glass breakage on ground-floor windows and doors that also have a beneficial side-effect of reducing sound transmission. Depending on how nice your building management is, you might even be able to get them to pitch in since it is technically an improvement to the structure.

If you aren't able to solve the problem from the outside by convincing the building management to redirect the water somehow, you can at least try to solve the problem from the inside by adding mass to the glass roof.

Adding mass to the panels by applying a window tinting film to the glass panels or a vinyl film to the aluminum support beams should at least help to dampen the noise and lower the frequency (by which I mean the pitch, not the number of drips per minute) of the sound.

There are films designed to prevent glass breakage on ground-floor windows and doors that also have a beneficial side-effect of reducing resonation generated by striking the pane. It's not going to silence someone knocking on it, but it should help to dampen the noise generated something so small as a water droplet. Depending on how nice your building management is, you might even be able to get them to pitch in since it could be spun as a security improvement to the structure.