It means the cat is bored
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i think it means they want attention, when my cat did this she wanted me to pet her or go to her so she would have me follow and show she wants to go out or have some food.
I assumed she just knew how cute she is and deliberately wanted to be even more cute so i would have to come to her, which i always did precisely for that reason.
Showing their belly means they trust you. If they let you rub their belly they really trust you.
What if you stick you face in their belly and go "wuzza wuzza wuzza"?

Freezie pops

It depends. It's like when a human says "I love you." In some cases it's time to blow them a kiss and cook them some crepes. In other cases it's time to double-check your safeword and tighten the straps.
😂
Check eyes. Dilated pupils. Combat mode.
👍
One of my cats lays on her back and stretches out when she's hot. If you try to scratch her belly, she will claw your arm off. So she has clearly communicated that I should not scratch her belly and that's an easy message to understand based on the scars.
My other cat loves belly scratches, but she prefers if I pick her up for them.
The easy thing to do is try various actions and then stop doing the ones that result in you getting your arm torn off, and whatever's left over, that's what the cat likes
What if you don’t figure it out before losing both arms?
Head cup and little scratch behind ear. Quality trust time, ignore incidental cat tum for now.
Where does he run off to? Me might be trying to bring you somewhere.
Just gets up. Runs off a bit. Looks back at me. Like I did something wrong. Cause I guess I did.
I think he's wanting to play as some others have suggested. Play with a fishing rod or wand. But no touchy .
Mine wants belly rubs. This goes on for a bit until he decides you are a chew toy now.
Belly rubs and blood. Did you try slow blinking at him before touching? Maybe he wants you to touch him but is nervous.
Sometimes he will do kitty winks back and forth with me. But tummy is off limits.
He has never liked that.
I think he wants to play with a wand toy. He seems open to that.
Belly trap!!
Sometimes i protecc, but mostly i attacc
Cat 🥰
Try getting a feather on a stick type toy and pulling it out when he does this. I'd say he wants to play, but doesn't want to engage your actual huge ape body when it comes down to it. In any case, it's a sign he considers you his human. He's really a beautiful cat.
I have a heavy cloth, like canvas, stuffed tube that I break out when he is on his back with crazy eyes. I know he wants to get a good "dig" in. I rub the tube on his belly and he'll latch onto it a tear into it like he's gotten some sweet prey. I'll even hold one end and drag him around the floor and rotate him while he furiously kicks and chews it.
My cat does this when she’s happy. She’ll fall asleep like that with a literal little smile on her face in the sun and when I see it I explode because it’s so damn cute. She’s also an old girl so I have to kinda make sure she’s breathing these days and didn’t literally go belly up and give up the ghost on me 😭😭
Pets really nailed down the manipulation through cuteness
They've reached the apex of survival. Find the top life form then latch onto them and get them to serve and fuss over you.
Violence
Put on a thick leather work glove and wrestle him.
I used to do this with my giant Main Coon. I could feel his teeth trying to bury themselves in my hand. Ahhhh!
You need thicker gloves!
Cats will often show you their belly as a sign of trust, as it makes them vulnerable. Some cats love to have their bellies rubbed, others view it as a breach of trust and will shred you, even though they flopped over. If it's a cat you don't know, the best thing is to just reach down and scratch the top of their head around the ears. If you want to see how far you can push it, give them scritches under the chin, move down to the upper chest, and inch your way lower to see how far they're okay with going.
My friends watching me scratch the floor in the other room, look back at their cat, take another step and scratch the floor again
If I even approach with my hand he gets mad and runs off before I even make contact. He is generally fond of cheek rubs. But he won't even let me do that when he's on his back.
To me it sounds like it could be what some littermates do to eachother, he's calling you to play. Our cats will do this same thing, but to each other: Jade will first go groom Ciri's face for a bit, perhaps a little stranglehold here, or she flops down in front of her sister, asking her to jump on top and wrestle, a lot like what you've described in the post. YMMV obviously, you know your cat better than a stranger online etc., but my two cents from my experience with a lot of litters in the past, I've seen this before many times.
It can also be what comment above said, he could be just showing his trust to you, but since it's such a high stakes thing, he could be a little overstimulated and doesn't know what he actually wants, and just reacts like his instincts are telling him.
With my cat, it's an invitation to play fight.
So I put on an oven mitt, tickle her belly and she clamps down on it and tries to kill it.
But she doesn't extend her claws or actually bite down, and when I remove my hand she goes back to the position on her back. Which tells me she seems to enjoy it.
Maybe he's asking you to give it a go, too?
Blood (yours)
hes telling you he likes you and is happy youre here and doing whatever youre doing.
not all cats showing belly want belly touched, simple as.
Yeah, my cat just wants effusive praise when she does this, she doesn't want me touching her.
My cat does this for belly rubs... Her software is bugged and doesn't have a limit on belly rubs. Also to scratch her back on the carpet. She will also let me spin her like a beyblade while doing this for some reason and keep laying on her back for more belly rubs
Every cat is different. One of ours demands belly rubs like this.
Another one cannot tolerate being touched in any way. You go to pet her and she's like:
They're apologizing. Or belly rubs.
If they lie like that peacefully and contently then it's because they find it comfortable.
If they're active and trying to get your attention, but don't want pets, then it's because they want to play.
My Siamese Mama Bear always wanted me to give her a really rough, all-over rubbing. She could take as much as I wanted to give. I always surrendered before she did.
It’s a trap!!
My old cat used to love belly rubs, and would never attack. Miss her so much.
My new cat doesn’t offer. I don’t think she understands the concept. She was a stray and still pretty young. Maybe she will grow into it.
My adult cat wants to be pet when he does that. The kitten does it mostly when she's in trouble for something. Almost seems like asking for forgiveness when she does it, but I know it's a lie.