I have tried to duplicate the iOS calendar style using some of the open source components below:
Kal -it is very good and detailed, exactly like iOS calendar
Tapku - very big but nice
CK Calendar- only month, without EventKit integraion.
For Day and Week View.
Also this.
AB Calendar Picker - It is awesome with year control.
It is better to see how all of this is implemented and then do something on your own.
