OK OK, all is perfect now
Android calendar is synchronized with davdroid
Android contact is also synchronized with davdroid
sorry for the waste of time
I have a problem, it does not show the birthday of my contacts on the default calendar (zenui calendar asus zenfone).
I think the problem is not dependent on zenui calendar, because if I put the birthday on phone contacts or google contacts it works. But if I put the birthday of contacts DAVdroid it is not working.
Google is importing the birthdays automatically, but this is some kind of extra feature. Generally it’s not DAVdroids purpose to populate the calendar. It is only writing the synchronized contents to the corresponding Android storage. If you need this there is another small app that provides this feature, it was discussed here: https://forums.bitfire.at/topic/461/contacts-birthday-in-calendar-app
With calendar birthday adapter app it works