Depending on the extent of the under eye wrinkles, there are a several options, including the newest technology via non-invasive treatments and surgical treatments. If you have significant wrinkles that require surgery, the incision can be well camouflaged so that it is not visible. Please consult with a board certified specialist who can assist you with achieving the results you seek. 3-dimensional computer imaging can also help you visualize what you may look like afterwards and help you communicate with your surgeon the results you desire.
Surgery can't be done without causing a scar.
Cosmetic surgery is designed to minimize or hide scars. The real question is what precisely do you need to help you with your lower eyelid lines. You did not provide a photo so it is hard to directly answer you. In general it is best to start with the least invasive methods. Surgery may not be the first choice. Consider reposting with photos so we can help you with a more detailed answer.