Isometric immersions into 3-dimensional homogeneous manifolds

@article{Daniel2005IsometricII,
  title={Isometric immersions into 3-dimensional homogeneous manifolds},
  author={Beno{\^i}t Daniel},
  journal={Commentarii Mathematici Helvetici},
  year={2005},
  volume={82},
  pages={87-131}
}
  • Benoît Daniel
  • Published 2005
  • Mathematics
  • Commentarii Mathematici Helvetici
We give a necessary and sufficient condition for a 2-dimensional Riemannian manifold to be locally isometrically immersed into a 3-dimensional homogeneous Riemannian 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 group Nil3, the universal cover of the Lie group PSL2(R) and the product… Expand

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