Surfaces in 3-dimensional homogeneous spaces
type: Dataset
description: The present dissertation deals with the study of minimal and constant mean curvature surfaces in 3-dimensional homogeneous spaces. In a first part, we establish Sym-Bobenko formulæ for constant mean curvature 1/2 surfaces in H^2xR and minimal surfaces in the Heisenberg group, and give examples of construction of such immersions using the DPW method. We also show that certain symmetry properties are shared by sister or cousin surfaces, which implies the existence non rotational entire graphs of constant mean curvature 1/2 in H^2xR with a vertical end.In a second part, we treat in more details the study of vertical ends of constant mean curvature 1/2 immersions in H^2xR. We endow a particular family entire graphs with a structure of smooth manifold and deduce an analogue in H^2xR to a theorem by A. E. Treibergs in the Minkowski space. We are also interested in deforming rotational annuli. A direct consequence is the existence of immersed non rotational annuli, and in particular we construct annuli with ends that do not have the same axis. Finally, we describe the Nœther invariants corresponding to isometries of the ambient homogeneous space for minimal and constant mean curvature surfaces. To do so, we use the formalism of contact geometry which allows general and explicit formulæ. We then study the evolution of Nœther form under the action of isometries in homogeneous spaces. We compute these invariants in the case of deformed annuli in H^2xR, and in the case of horizontal annuli in Heisenberg group
identifier: NNT: 2011PEST1007
issued: 2026-05-27T19:12:09.620919
language: fr
modified: 2026-05-27T19:12:09.620925
contact point: Organization
  fn: CCSD
keyword: constant-mean-curvature-surfaces
keyword: contact-structure
keyword: espaces-de-modules
keyword: espaces-homogenes
keyword: formules-de-sym-bobenko
keyword: homogeneous-spaces
keyword: infoeu-reposemanticsdoctoralthesis
keyword: invariants-de-noether
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: moduli-spaces
keyword: noether-invariants
keyword: structure-de-contact
keyword: surfaces-a-courbure-moyenne-constante
keyword: sym-bobenko-formulae
keyword: theses
landing page: https://theses.hal.science/tel-00672332

Surfaces in 3-dimensional homogeneous spaces
type: Distribution
format: HTML
issued: 2026-05-27T19:12:09.720265
modified: 2026-05-27T19:12:09.589598
access URL: https://theses.hal.science/tel-00672332

test_moissonnage_selune
type: Agent