I made this object with Illustrator and Imported it to PS.
What I want is to make a shiny effect by applying a Curves layer.
The problem is after I applied the Curves layer, the black strokes become badly defined as you can see below.
Note: my object is on one layer.
How can I make sure that the strokes remain as well defined as in the original image?
You need the rings to be on a different layer to the gradient. That would be a no brainer for all sorts of reasons, just one of which you have discovered.
The problem with using the single layer is the anti aliasing is needed to make the rings look nice on a raster image, but the AA is being affected by the radical Curves layer. With separate layers, you could keep the AA on the rings.
Using 16 bit and turning anti aliasing off will help minimize the effect.