Curved coordinates

Questions
,
1

Just want to draw a few curved coordinate lines. Can’t find a useful tool for this. Thanks for a tip.
Bernd

2

One way to get an informative picture is with ContourPlot:

Show[ContourPlot[x^2 - y^2, {x, -2, 2}, {y, -2, 2}, Contours -> 20, 
  PlotPoints -> 50, ContourShading -> False, ContourStyle -> Black],
 ContourPlot[x y, {x, -2, 2}, {y, -2, 2}, Contours -> 20, 
  PlotPoints -> 50, ContourShading -> False, ContourStyle -> Red]]

Disappointingly, this concise version shows only the 0-level contours:

ContourPlot[{x^2 - y^2, x y}, {x, -2, 2}, {y, -2, 2},
 Contours -> 20, ContourShading -> False]
3

Hi Gianluca, Hi Luca, it looks very good. Yesterday I tried for some hours with Contourplot. But without much success. Don’t use mathematica every day, and then it’s not easy to use the many options correctly.
Italy is hard hit by Corona. We all suffer with you. I hope that your family is well. Best regards Bernd

4

Hello Gianluca, I have skimmed my text again and noticed that I did not thank you at all. Sorry. I would like to make up for that: Thanks for the helpful tip. - I am a retired physicist, interested in general relativity.
I wish you all the best and remain with best regards
Bernd

5

You are welcome. Best regards from the Italian covid-captivity