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

2005/11/21 by Marcos P. Cavalcante, Jorge H. de Lira, Cavalcante, Marcos P. de A. +1
Mathematics · Physics and Astronomy · #53A10 #53C42 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0511530

openalex publication_date 2005/11/21 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

It is proved that the holomorphic quadratic differential associated to CMC surfaces in Riemannian products \mathbbS²×\Rr and ℍ²× \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.

Citations

• Surfaces of annulus type with constant mean curvature in Lorentz-Minkowski space

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