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Scene: 3rd level PC's have moored their ship to the pier. Arrived on Pirate Island.
The walk up a steep 80' steep slope, to the Large Pirate Building. Pirates are in a building at the top of the slope. The door is slightly ajar, and the pirates are hiding with full cover.
When the PC's enter within 30'. The make perception checks dc23.
Failure indicates surprise.
5 Pirate, Sailor CR 1/2 +1 Cleric1/Bard1 +1 Barbarian1/Cleric1 (Besmara)
rush out of the building Seal Team 6 style, and surround the PCs.
Their tactics are don't let the Pcs gain the higher ground, but 5' downhill for a flank.
Initiative is rolled. Pirates surround the PC's. While the PC's are somewhat still in their formation.
Then the Pirate/Bard casts Grease on a cluster of PCs.
A PC fails, and slides down the steep slope...
Do the Pirates get AOO while the PC's slide down between them?
Steep Slope: Characters moving uphill (to an adjacent square of higher elevation) must spend 2 squares of movement to enter each square of steep slope. Characters running or charging downhill (moving to an adjacent square of lower elevation) must succeed on a DC 10 Acrobatics check upon entering the first steep slope square. Mounted characters make a DC 10 Ride check instead. Characters who fail this check stumble and must end their movement 1d2 × 5 feet later. Characters who fail by 5 or more fall prone in the square where they end their movement. A steep slope increases the DC of Acrobatics checks by 2.
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First of all, the sliding down the slope doesn't seem to be RAW in any way, but for fluff it's of course your decision.
Secondly personally I wouldn't give the Pirates AoO for that.
My reasoning is the ruling of Bull Rush: You need 2 extra Feats (Imp. Bull Rush und Greater Bull Rush) until the forced movement of a Bull Rush on an opponent provokes AoO."Benefit: You receive a +2 bonus on checks made to bull rush a foe. This bonus stacks with the bonus granted by Improved Bull Rush. Whenever you bull rush an opponent, his movement provokes attacks of opportunity from all of your allies (but not you)."
Grease is a Level 1 Spell; that would make it (of course only in that specific situation) waaay stronger.
Ok, I'll go with that. No AoO, for sliding down adjacent squares.
Seems there's a little difference from a 2nd edition grease spell, and pathfinder.
Would the PCs slide down the slope at all?
If the PC's do slide down the slope, into a square already occupied with pirates, the pirates in those squares obviously get AOO. It'd be like a very botched overrun.
Situations in which "forced" movement (i.e., someone or something pushing, pulling, or otherwise moving you against your will) provokes an AoO are pretty rare in the rules. In nearly every case where it happens, it requires an extra feat or two.
there's PLENTY of situations where 'environmental' effects may cause 'forced' movement ('forced' indirectly, not directly via another character, which would be a CMB),
try sundering the branch somebody is standing on, on collapsing the cliff edge they are on, etc.
straight up falling should provoke per RAW.
sitting tied up on a horse that is moving is provoking movement, as is on a levitating force disk, or clockwork escalator.
re: grease, there's nothing in RAW to suggest that you would move laterally if the surface you are standing on (now prone) is a slope.
sure, you COULD imagine it is the type of grease that may allow that, but the spell doesn't say that happens,
and it could just as well be a type of grease that just hampers normal walking/running, and makes people tend to fall,
but isn't enough to cause you to slide into other (lateral) squares. So if you stick with what the spell actually says it does, you should be good.
=no lateral movement whatever the slope, thus no AoO (unless they have a special ability to target characters when they are tripped)
which would mean that there isn't enough lubrication to let ANY slope move a character laterally once they are prone (which has more friction than standing)