Hi. If there is purely a pigmentation issue then u can try some under eye creams which are available. u can go to a dermatologist and get a proper assessment and possibly a peel done which would cater to the under eye region. If it is due to a vascular cause (the darkness that u see), it will not improve with any method at all. Drink adequate amount of water and avoid late nights, and continuous eye strain while working on a laptop/computer etc. Are some general measures.
Dr. Zubin Mandlewala