Examples and structure of CMC surfaces in some Riemannian and Lorentzian homogeneous spaces

Details Examples and structure of CMC surfaces in some Riemannian and Lorentzian homogeneous spaces Examples and structure of CMC surfaces in some Riemannian and Lorentzian homogeneous spaces

2005-11-21

arxiv.org/abs/math/0511530v1

Mathematics

Differential Geometry

38 pages

Scientific paper

It is proved that the holomorphic quadratic differential associated to CMC surfaces in Riemannian products $\mathbb{S}^2\times\Rr$ and $\mathbb{H}^2\times \Rr$ discovered by U. Abresch and H. Rosenberg could be obtained as a linear combination of usual Hopf differentials. Using this fact, we are able to extend it for Lorentzian products. Families of examples of helicoidal CMC surfaces on these spaces are explicitly described. We also present some characterizations of CMC rotationally invariant discs and spheres. Finally, after establish some height and area estimates, we prove the existence of constant mean curvature Killing graphs.

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