Is it submission? Desire to have her tummy rubbed? (I don’t think so with this one - attempts to do this often earn an irritated swipe) Or just a cat way of saying hi?
Mine does this too. It’s like she just suddenly goes limp.
Yeah, so answer the OP’s question.
-FrL-
My parent’s cat does as well. In his case, it’s because he loves being scratched (roughly, even) on his side. He gets so into it, he’ll start crawling his way across the carpet, while still on his side. It’s hilarious.
Cats are, science tells us, in league with the Devil. This one is obviously trying to devour your soul.
Is it a sign of submission?
“Here’s my belly, I couldn’t possibly mean you any harm!”
I dunno, when we brought a kitten home as company for an older male cat, her response whenever he approached was to flip over in about 1.2 microseconds because this allowed her to use all four paws (and attached claws) in defense. Perhaps the cat sees you as a huge potential attacker and is getting into the optimal defensive position. Or he just wants a tummy rub.
My little monkey does this as well (ok she’s a cat, we just call her monkey), and gets equally swipey when rubbed on the lower tummy, she seems to do this as a reflex when ever she’s touched there, so I think it may just be quite a sensitive area.
I’ve always felt it was her way to greet me when she was feeling a tad pathetic and lazy, makes us come to them rather than them do the work. It’s quite successful too as neither I nor the boy can resist a prone kitty.
This site seems to agree with me: cite
And Promethea, is she a Burmese, she looks very similar to my little one?? 
It is a invitation to play, either for petting or play fighting. From watching kittens the one on the ground is the one in defensive attack mode, able to bring 4 claws and one set of jaws to bear on the attacker, while the attacker must use at least 2 paws for locomotion to make up the final distance between them and to start the attack.
Our little orange guy does this all the time to us to have his belly rubbed. He does it to the other cat when they’re wrestling so he can pretend to disembowel him.
In other words, either to allow you to pleasure him or to disembowel you. You pays your money, you takes your chances.
Fear, pure unadultered fear
For cats, “belly up” is the attack position; its the only position where they can use all their weapons at once. Exposing its belly is not a submissive posture in a cat, its an agressive (or playful) one, in stark contrast to the behavior of a dog.
Now, my cat used to go “flop” when I would head out the door, but it was because he knew that by being irresistably cute I would pause on my way out to pet him.
One of my ex’s cats does the “tickle my tummy” thing, but the odd thing is, she only does it outdoors. I’ve never seen her roll on her back indoors, yet every time I meet her in the garden, over she goes. I’ve never understood that.
Sorry, no pics at the moment.
Nope, she’s a black moggy born of a ginger/ white stripey mum and unknown Dad. I Burmese cats though - any pics of yours?
We think it’s submission. Our little Hestia does this when our old, crotchety Midnight passes by and hisses at her. She does NOT do it when she wants to play, as she often does with Clarence.
All respect to hello again, but I don’t believe that “cat on back” is in attack position. Cats DO attack with both front paws (pulling in) and back paws {kicking out, an active scratching and potentially disemboweliung move), but this also exposes their vulnerable bellies, and I’ve never seen an alert and hostile cat do it – they stay upright, backs raised, hair all puffed out (to make themselves seem larger), ears back (out of danger), and alert, always facing the danger spot. A cat on its vack is putting itself in a very vulnerable position, and is signifying submission and/or asking for a belly rub.
This is what my understanding has always been. However there’s also a little trigger that goes off at some point where “soft tummy getting rubbed = kitty about to get stomach attacked” and the cat will go from lying there purring happily away to suddenly latching on to your hand and scratching/biting. It’s an instinctive reaction to the position; exactly how much a given cat will let you get away with is up to the individual.
http://www.catcaresociety.org/social.html
Read down to “Defensive aggression.” I may have overstated the extent to which this is a purely agressive posture, but it is NOT a submissive posture.
I have two cats that fight all the time* and I am frequent witness to the behavior; cats will get to their sides, legs contracted (what we call “chambered” in Karate class!) prepared to fire on all cylinders.
*both fixed, one male, one female, both are known to instigate; the male is front-declawed.
From your cite:
Sounds like what I described above, and not at all like a cat lying on the ground, belly up and all legs spread.
And from this site:
http://home.ivillage.com/pets/cats/0,,mj2z,00.html
Bolding mine – notice that only after battle is engaged will the cat roll onto its back as a defensive move.
We may be talking at cross purposes. There are many positions a cat can take which include lying comfortably on its back “airing out the belly” as we call it. My point is only that such posture is not inherently submissive, as it is in dogs, and probably not submissive at all. As your cite notes, moving to the side or back is not intended as a submissive posture that thwarts an attack. My cite also notes that cats do not form firm hierarchies of dominance/submission.
A better description of what I was imagining is in the “intermale aggression” section, actually (emphasis added):
If an attack occurs, the attacker will usually jump forward, directing a bite to the nape of the neck, while the opponent falls to the ground on his back and attempts to bite and scratch the attacker’s belly with his hind legs.
My mom’s cat (well, actually she is my cat, but I didn’t have the heart to take her with me when I moved out, since she has acreage to run around on) does the same thing, but the scratching/biting thing is her being playful (she’s gentle). Another sign of playfulness is when she bats her tail around, like she’s using it as a lure to catch bait.
My suggestion, when your cat flops, would be to get down on all fours and start stalking your cat. If she’s like mine, you’ll get a lively game of hide-and-go-seek out of it (I usually win).