What can be done to correct these indentations under my eyes when I smile? (Photo)

this is common for people as they get older, fillers, lasers and deep microneedling RF like morpheus help this. nothing willl fully get rid of it, surgery/mid face lift/lower bleph is an opportunity.  at home dermarolling (see link to emeragecosmetics.com where we do free skincare consults daily) can also help.
There are many things you can do to treat under eye hollows and dark circles. A surgical option to remove skin and/or fat will be the best long term.  However, non invasive less downtime options such as fillers, lasers, microneedling/PRP, cosmelan peels and stem cells can all help give some improvement. I suggest. You get a formal consultation to see what is best for you and your goals.

Unfortunately, from the photo provided it is really difficult to say for certain, and an in-person examination would allow for manipulation and palpation for a more definitive evaluation. However, it does appear that your problem, in experienced hands, can be addressed with the proper use and choice of a filler, either placed in the cheek region, which would secondarily pull smoother the area that disturbs you or the use of a different filler placed directly into the depression itself to elevate it and smooth it in that fashion. Your physician may first opt to use a small amount of salt solution or diluted anesthetic into the region to gauge the benefits and demonstrate them to you before actually performing the actual treatment. This is an area only for experienced physician injectors, so do your due diligence well for vetting the injector.. Best of luck and stay well.  

It is difficult to advise a treatment from the photo provided.  If the concern is due to volume loss then the appropriate filler should be helpful.  If it is from skin laxity you could consider skin tightening procedures such as FaceTite  with Morphues8 treatments.

It's difficult to tell from your pictures whether or not these indentations are when you're in a full smile or part of your anatomy. That being aaid, I would be careful with injectable fillers or fat around your eyes just to correct a fold that is present when you are smiling.  This may leave you with a lump instead of a depression. I would recommend you see a board certified plastic surgeon specializing in facial rejuvenation for an adequate examination.  Good luck!

It is difficult to tell from the photos whether you have true or pseudo-tear troughs.  In both cases they can be improved with fillers.  It is important to distinguish between the two conditions as the placement of the filler and the type of filler used is usually different. Remember small volumes in this area are usually sufficient and there is no need for over correction.  Good luck!

Hello.Although there are limitations in the photos but fillers in cheek area will do the job.Consult with an expert.Best

Although it is very difficult to tell much from your pictures, it appears the you have a low origin of the medial muscles leaving a hollow between the fat around the eye and the cheek. If so, this is easily corrected with a filler such as Juvederm Voluma or Radiesse. However, this requires an expert who understands the anatomy.