Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606253 | Differential Geometry and its Applications | 2011 | 8 Pages |
Abstract
We describe all surfaces in S2ÃR and H2ÃR with holomorphic Abresch-Rosenberg differential (originally defined in Abresch and Rosenberg, 2004 [1]) and non-constant mean curvature. We prove that the horizontal slices of these surfaces are the level curves of the mean curvature H, whose projections determine either a polar system of geodesic rays and circles in the base (rotational surfaces) or an orthogonal system of ultra-parallel geodesics and equidistant curves in H2. The non-rotational surfaces in H2ÃR extend to regular graphs over H2; these are new examples of complete surfaces in H2ÃR with constant Gaussian curvature Kâ(â1,0).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Henrique Araújo, Maria Luiza Leite,