The way there was a bit difficult. The reviews here were mostly promising, but worry I made the battery life.
And exactly this problem turned out.
But before I write long texts here ... here is my solution:
Maintains synchronization for Google+ account, and the battery :) This can be reactivated if required.
(Settings -> Accounts -> Save Reset -> Back up my data check out)
This feature probably runs continuously, and thus verbrucht much battery.
Even more so since I have no LTE contract, and me HSDPA + enough, I put the network mode GSM / WCDMA (connect automatically)
This can be found at Mobile networks.
Now the battery lasts two days .... everything is going great. A great mobile phone !!!!