Your eyes should be open, and you should try to keep your eyes at the place of sujood. I'm fairly certain of this, just lemme try to look for a hadith to make sure.
edit- couldn't find a hadith, but this website explains everything about salah.
http://darulislam.info/mod-ContentEx...ay-ceid-2.html
from it i got "6. When standing for Salat, keep you eyes looking at the spot where you make your Sajdah. Abstain from looking to your right and left, or front."
"7. In the state of Ruku', the ayes should be looking towards the feet. "
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