The Bonnet problem for surfaces in homogeneous 3-manifolds

Details The Bonnet problem for surfaces in homogeneous 3-manifolds The Bonnet problem for surfaces in homogeneous 3-manifolds

2006-12-26

arxiv.org/abs/math/0612766v1

Mathematics

Differential Geometry

Scientific paper

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^2xR or S^2xR is uniquely determined pointwise by its metric and its principal curvatures if and only if it is not a minimal or a properly helicoidal surface. In the remaining three types of homogeneous 3-manifolds, we show that except for constant mean curvature surfaces and helicoidal surfaces, all simply connected real analytic surfaces are pointwise determined by their metric and principal curvatures.

Affiliated with

Also associated with

No associations

Rating

The Bonnet problem for surfaces in homogeneous 3-manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Bonnet problem for surfaces in homogeneous 3-manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Bonnet problem for surfaces in homogeneous 3-manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-203161