Looking at some built-in classes, I would say you just need to #import the AppManager.h file yourself. Here are the paths you probably need (you probably don't need all of them!):
../iphone/Classes/Rhodes.h ../iphone/Classes/AppManager/AppManager.h ../iphone/Classes/RhoMainView.h ../shared/common/RhodesApp.h
Did you manage to solve this problem? I have updated now from Rhodes 184.108.40.206 to 4.0.0 and i am having the same issue as you explained. I need to use [Rhodes sharedInstance], but #import "Rhodes.h" does not work in my native extension impl/__Singleton.m file. This was no problem when I used it in Rhodes 220.127.116.11.
Did you found any fix for this?