can curves be parallel to each other？

[mg1912]

they can. when we are talking about parallel, it can be concluded into 2 situations, the parallel of straight lines and the parallel of curves. the situation of straight lines is just a particular example of paralle.
there are many example of parallel of curves, for example, concentric circles, tortuous railway and so on. the essential character of parallel is a certain unchange distance, the concentric circles is a good example of this. at the same time circles are also curves. so curves can be parallel to each other.

[Jamma]

Even straight parallel lines can intersect in non-Euclidean geometry, what's new?

[HallsofIvy]

they can. when we are talking about parallel, it can be concluded into 2 situations, the parallel of straight lines and the parallel of curves. the situation of straight lines is just a particular example of paralle.
there are many example of parallel of curves, for example, concentric circles, tortuous railway and so on. the essential character of parallel is a certain unchange distance, the concentric circles is a good example of this. at the same time circles are also curves. so curves can be parallel to each other.
Are you asking or simply asserting?

You are going to have to tell us what you want to mean by "parallel". The usual definition of "parallel lines" is "lines that do not intersect". Of course there exist curves that do not intersect. Another is "have constant distance apart"- "equidistant lines". There exist curves of that kind: two concentric circles with different radii are, as you say, equidistant. (Of course, in non-euclidean geometry, equidistant line may not be parallel.