Edit: Even after i changed your manifest it shows a white page. Are you sure you have enabled the GoogleMaps api with your project inside the google console?
Register your app in Google developer console: https://console.developers.google.com
You need to enable Google Maps Android API.
Then click on Credentials -> Create Credentials -> API Key -> Android Key.
You should get a key that looks like: AIzaSyCmFHamGE0O0BvxxxxxxxxXbTCSrjFVg-Q