Look for pictures of bahia and paspallum to see if it might be one of those. There are also a couple strands of what looks like bermuda. In any case, the grass is doing poorly in that location. If you would like a turf that is more dense than that, look at the St Augustine varieties noted for performance in the shade. For example, Floratam is a variety that is suggested for performance in full sun, not shade; however, it does better than what you have in the shade.

I'm not an expert, but isn't that zoysia? Mine is a warm season grass with about that appearance in NC, it slowly fills in gaps and migrates, it's in about 50% shade under tall trees, gets large spot in the spring and never grows more than about 60 inches even if I miss mowing.

Does look like Zoysia. 'Compadre' or 'Zenith' Zoysia seed available many places on-line.

Zoysia grass seed is NOT available or out of stock from the major seed producers this year because of a 2019 crop failure across the U.S. It is available on Amazon but the pricing is extremely high and averages $40-$50/lb. I could never afford that! I have already used about 30# on my property and I'm not done yet. I have opted for bermuda seed for the sunny areas and centipede seed for the sun/shade areas. Being that I am up against many weeds and poor sandy soil, it could be at least 1-2 years before I have a decent lawn. Thanks for all your comments.

You won't need seed for zoysia. It spreads puh-LENTY. That grass in the picture needs fertilizer. Here's a picture of some zoysia fertilized with alfalfa pellets.

The surrounding grass looks like yours. The grass in the center was fertilized in mid May with a handful of alfalfa pellets (rabbit chow). The picture taken in mid June. Thanks to mrmumbles for posting the pic way back when.

If those are oak leaves amongst your grass blades you will have a tough time growing any type of grass there. Try some confederate jasmine, or etc ground covers.

Thanks but ground cover is the last thing that I want. I've had plenty of experience with it and it will take over your whole lawn if you let it. I was advised by a very reputable seed company to plant centipede grass in those areas. It will certainly be a challenge.