What are the US definition and restrictions on aerobatic flight?
Aerobatic flight is "an intentional maneuver involving an abrupt change in an aircraft's attitude, an abnormal attitude, or abnormal acceleration, not necessary for normal flight."

According to the FAA (91.303), no person may operate an aircraft in aerobatic flight:


Over any congested area of a city, town, or settlement;
Over an open air assembly of persons;
Within the lateral boundaries of the surface areas of Class B, Class C, Class D, or Class E airspace designated for an airport;
Within 4 nautical miles of the center line of any Federal airway;
Below an altitude of 1,500 feet above the surface; or
When flight visibility is less than 3 statute miles.


Aerobatic flight is sometimes considered to be flight with more than 30 degrees pitch or more than 60 degrees bank. This is incorrect. It applies to wearing a parachute. (FAR 91.307)

A normal category aircraft is certified for the following "non-acrobatic" operation: Stalls, lazy eights, chandelles, and steep turns, in which the angle of bank is not more than 60°.

A utility category aircraft is certified for spins (if approved for plane), lazy eights, chandelles, and steep turns, or similar manoeuvres, in which the angle of bank is more than 60 degrees but not more than 90 degrees. 

An acrobatic category aircraft is required for other aerobatics.