Omitting the dot and not fully qualifying the package/class name will work if and only if the specified class is not part of a subpackage within your application.
If your application package name is com.example.myapp, and you have an activity class com.example.myapp.MyActivity:
android:name="MyActivity" will work.android:name=".MyActivity" will work.android:name="com.example.myapp.MyActivity" will work.
But if you have the same application package and an activity class in a subpackage within your source tree such as com.example.myapp.myactivities.MyActivity things change.
android:name=".myactivities.MyActivity" will workandroid:name="com.example.myapp.myactivities.MyActivity" will workandroid:name="MyActivity" will not workandroid:name="myactivities.MyActivity" will not work
3 doesn't work because that will infer that the class name you mean is actually com.example.myapp.MyActivity like in the first example above. A class with this name won't be found and you'll get an error.
4 doesn't work because it looks like a fully qualified class name, that is the system will interpret it to mean that myactivities.MyActivity is the fully qualified name itself, not the real name of com.example.myapp.myactivities.MyActivity.
You need the leading dot here to clarify that you're using a relative path, not an absolute path. If you specify just a class name with no package info at all, the system infers that the class is at the root of your application package hierarchy.
