simple inexpensive cover that I picked up on Amazon made by Cimo.
Seems to provide good protection and I don't feel like I'm going to drop my phone when I'm holding it
Amazon.com: Cimo S-Line Back Case Flexible TPU Cover for Samsung Galaxy Note 3 - Clear: Cell Phones & Accessories
Galaxy Note 3 Case Slim S-Line | Galaxy Note 3 | Samsung | Brands | Cimo
Judging by the pattern, I probably have the same one in black. I bought it for the same reason: the longitudinal grooves on the original frame made the phone slip. Whereas the rubber sides of this case give me perfect grip.
Alas, it is heavy. It adds 28 grams to the 168 gram weight of the phone. We do metric in Australia, but you can appreciate by the ratio of the two numbers that the case adds an extra 17% to the weight of the phone. I first felt this in my wrist, the calculation came later.
Most of the weight is in the back cover, which I find superfluous. I prefer the original Samsung back. I'd like something lighter to give me good grip on the sides. But I'm a newbee with cases, so I don't even know what to look for.
Please help with the terminology. What would be the name of a case, which only goes on the side frame, without necessarily covering the entire back of the phone.