What was found
AIRCRAFT WAS NOT GROUNDED. EMERGENCY DECLARED. LANDING UNEVENTFUL. AIRCRAFT NOT OVERWEIGHT. DURING CLIMB THE RIGHT FUEL QUANTITY SHOWED 1000 LBS LOWER THAN THE LEFT WITH AMBER, "IMBALANCE" ILLUMINATED. THE DIFFERENTIAL INDICATION THROUGHOUT FLIGHT. MAINTENANCE ACCOMPLISHED BITE OF FUEL QUANTITY SYSTEM WITH NO FAULTS FOUND. ACCOMPLISHED STICK CHECK OF TANKS IAW AMM 28-41-00. TRANSFERRED FUEL, RECHECKED TANKS WITH STICKS AND COCKPIT INDICATION. FUEL INDICATION NORMAL AND WITHIN LIMITS.