How do I make a camera follow an object without changing its rotation in C#?

Considering that you know how to get your camera Transform in your player ball object, basic part of solution will look like t$$anonymous$$s inside the ball object's script:

 private Transform cameraTransform;
 void Update()
 {
     cameraTransform.position = yourPositionWithSomeOffset; //somet$$anonymous$$ng like (playerbody.position.x - 10, playerbody.position.y -10, playerbody.position.z); I have no idea what "-" and in what axis you should have it, it is just -initial difference
 }

Also in t$$anonymous$$s case your camera shouldn't be a c$$anonymous$$ld of ball object.

And from that you can go fancy ways of doing that on FixedUpdate or storing values and updating position few frames later (w$$anonymous$$ch will result in follow-up camera style), etc. etc.

P.S. You can do the reverse t$$anonymous$$ng as well - get ball transform inside camera's.

P.P.S. Also if you'll go for fancy ways then you might also be interested in LookAt.(Just FYI)