You have a number of choices: you can use:
- Insert>Curve>split Line
Experiment with each of them and check out online help to determine which is best suited for what you're trying to accomplish.
Thank you Mark. Wrap feature was what I was looking for. I did Wrap and then by selecting Deboss parameter worked really fine.
By using projected and split line I had curves drawn on the curved surface but the extrude cut was done a straight cut with not equal depth.