iPhone SDK 4 "Half curl page transition"

Are you talking about iBook style page turning animations? There's a blog piece about it here, with links to 2 GitHub projects with it:

http://oleb.net/blog/2010/06/app-store-safe-page-curl-animations/

It's not a transition, but a modalTransitionStyle. You can check the docs here: https://developer.apple.com/documentation/uikit/uiviewcontroller/1621388-modaltransitionstyle

If you create a new UIViewController, set its modalTransitionStyle to UIModalTransitionStylePartialCurl, and then presentModalViewController:animated: it, you'll get the desired "half curl page" effect.