Which properties preserve by isometry?

Question

I know that an isometry between two surfaces preserves the 1st fundamental coefficients, geodesic curvature, and Gaussian curvature.

I wonder that how about the curvature and torsion of a curve on the surface, and 2nd fundamental coefficients?

I can’t find any counterexample and prove this question

Give some advice or comments! Thank you!

Answer 1

Hint Consider an isometry from a subset of a plane in $\Bbb R^3$ to a subset of a cylinder in $\Bbb R^3$.