Isometric immersions into 3-dimensional homogeneous manifolds

Details Isometric immersions into 3-dimensional homogeneous manifolds Isometric immersions into 3-dimensional homogeneous manifolds

2005-03-23

arxiv.org/abs/math/0503500v1

Comment. Math. Helv. 82 (2007), no. 1, 87-131

Mathematics

Differential Geometry

38 pages, 1 figure

Scientific paper

We give a necessary and sufficient condition for a 2-dimensional Riemannian manifold to be locally isometrically immersed into a 3-dimensional homogeneous manifold with a 4-dimensional isometry group. The condition is expressed in terms of the metric, the second fundamental form, and data arising from an ambient Killing field. This class of 3-manifolds includes in particular the Berger spheres, the Heisenberg space Nil(3), the universal cover of the Lie group PSL(2,R) and the product spaces S^2 x R and H^2 x R. We give some applications to constant mean curvature (CMC) surfaces in these manifolds; in particular we prove the existence of a generalized Lawson correspondence, i.e., a local isometric correspondence between CMC surfaces in homogeneous 3-manifolds.

Affiliated with

Also associated with

No associations

Rating

Isometric immersions into 3-dimensional homogeneous 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 Isometric immersions into 3-dimensional homogeneous manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Isometric immersions into 3-dimensional homogeneous manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-135174