No, it is not correct to push the right handlebar while leaning left in a corner with a motorcycle at high speeds. The correct technique for cornering on a motorcycle involves countersteering.
Countersteering is a technique used to initiate a turn on a motorcycle. To turn left, you would actually push the left handlebar or apply pressure to the left side of the handlebar, which causes the front wheel to momentarily steer to the right. This slight steering to the right initiates a lean to the left, allowing you to corner smoothly.
The reason for this counterintuitive action is due to the gyroscopic effect of the wheels. By momentarily steering in the opposite direction of the intended turn, the bike leans into the corner and maintains stability throughout the maneuver. Once the lean is initiated, you can maintain control and adjust your position within the corner by modulating the throttle, body position, and applying subtle steering inputs.
It's important to note that cornering techniques can vary depending on the specific motorcycle model, rider preferences, and road conditions. It's always a good idea to consult your motorcycle's manual or receive training from a professional instructor to learn the correct techniques for safe and effective cornering.