The Bonnet problem for surfaces in homogeneous $3$-manifolds
The Bonnet problem for surfaces in homogeneous $3$-manifolds
We solve the Bonnet problem for surfaces in the homogeneous 3-manifolds with a 4-dimensional isometry group.More specifically, we show that a simply connected real-analytic surface in H 2 × R or S 2 × R is uniquely determined pointwise by its metric and its principal curvatures if and only if …