TeX-fold-mode is here to fold environments and macros (for example replacing
\lambda with a Unicode lambda or hiding a long proof).
outline-minor-mode is what you need, as you stated in the comments, but you shouldn't have to set the heading levels yourself, AUCTeX should take care of that for you.
If the key mapping is a problem to you, the easiest way to change it is to change the prefix-key for outline-mode.
This solution is described on EmacsWiki, where I found the following code snippet (to be added in your
(lambda () (local-set-key "\C-c\C-@"
The above snippet will actually do nothing in AUCTeX, but you can replace
\C-c\C-@ with any sequence of keys you like.
The shortcuts will then use that key sequence instead : for example, to move to the next visible heading, you'll use
<your key sequence> C-n.
You'll find on EmacsWiki many other options to change the keybindings, as well as suggestions for the choice of keys (but you'll probably need to figure out what key to use yourself, due to the many keybindings needed by AUCTeX).