Isometric immersions into 3-dimensional homogeneous manifolds
From MaRDI portal
Publication:863620
DOI10.4171/CMH/86zbMath1123.53029arXivmath/0503500MaRDI QIDQ863620
Publication date: 5 February 2007
Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0503500
isometric immersionsGauss and Codazzi equationsRiemannian connection3-dimensional homogeneous manifold
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Local submanifolds (53B25) Non-Euclidean differential geometry (53A35)
Related Items
Unnamed Item, Constant mean curvature isometric immersions into \(\mathbb{S}^2\times\mathbb{R}\) and \(\mathbb{H}^2\times\mathbb{R}\) and related results, Slab theorem and halfspace theorem for constant mean curvature surfaces in \(\mathbb{H}^2 \times \mathbb{R}\), Construction of minimal annuli in \(\widetilde{\mathrm{PSL}}_2(\mathbb{R},\tau)\) via a variational method, Conjugate plateau constructions in product spaces, Uniqueness of constant mean curvature spheres, Isoparametric hypersurfaces of Riemannian manifolds as initial data for the mean curvature flow, Total mean curvature surfaces in the product space and applications, Helix surfaces in the special linear group, Willmore-like tori in Killing submersions, Compact surfaces of constant Gaussian curvature in Randers manifolds, Delaunay surfaces of prescribed mean curvature in \(\mathrm{Nil}_3\) and \(\widetilde{SL_2}(\mathbb{R})\), Jacobi osculating rank and isotropic geodesics on naturally reductive 3-manifolds, Surfaces of orthonormal frame bundle with Wagner lift metric, Unnamed Item, The Gauss map and second fundamental form of surfaces in a Lie group, The Dirichlet problem for constant mean curvature surfaces in Heisenberg space, A characterization of constant mean curvature surfaces in homogeneous 3-manifolds, On complete submanifolds with parallel normalized mean curvature in product spaces, A Hopf theorem for non-constant mean curvature and a conjecture of A. D. Alexandrov, Elasticae in Killing submersions, Integrable deformation of critical surfaces in spaceforms, Complex and Lagrangian surfaces of the complex projective plane via Kählerian Killing \(\mathrm{Spin}^c\) spinors, Constant mean curvature spheres in homogeneous three-manifolds, Rotational symmetry of Weingarten spheres in homogeneous three-manifolds, Capillary immersions in \(\mathbb {E}(\kappa , \tau )\), Three-dimensional homogeneous critical metrics for quadratic curvature functionals, Delaunay surfaces of prescribed mean curvature in Berger spheres, Invariant surfaces in \(\widetilde{\mathrm{PSL}}_{2}(\mathbb R, \tau)\) and applications, Constant angle surfaces in the Lorentzian Heisenberg group, Willmore surfaces and Hopf tori in homogeneous 3-manifolds, On the moduli space of isometric surfaces with the same mean curvature in 4-dimensional space forms, Constant angle surfaces in Lorentzian Berger spheres, Finite index operators on surfaces, Simons type equation in \(\mathbb S^{2}\times \mathbb R\) and \(\mathbb H^{2}\times \mathbb R\) and applications, Isometric immersions into warped product spaces, On \(H=1/2\) surfaces in \(\widetilde{\mathrm{PSL}}_2(\mathbb R,\tau)\), Existence of isometric immersions into nilpotent Lie groups, Extensions of the duality between minimal surfaces and maximal surfaces, Parabolic stable surfaces with constant mean curvature, All solutions of the CMC-equation in \({\mathbb H^n\times\mathbb R}\) invariant by parabolic screw motion, Totally geodesic hypersurfaces of four-dimensional generalized symmetric spaces, A fundamental theorem for submanifolds of multiproducts of real space forms, When strictly locally convex hypersurfaces are embedded, Constant mean curvature graphs on exterior domains of the hyperbolic plane, Minimal surfaces in \(\widehat PSL_2(\mathbb R)\), Helix surfaces in the Berger sphere, Properly embedded surfaces with prescribed mean curvature in \(\mathbb{H}^2 \times \mathbb{R}\), Height estimates for constant mean curvature graphs in \(\mathrm{Nil}_3\) and \(\widetilde{PSL_2}(\mathbb{R})\), Dual quadratic differentials and entire minimal graphs in Heisenberg space, Unnamed Item, Cylinders as left invariant CMC surfaces in \(\operatorname{Sol}_3\) and \(E(\kappa,\tau)\)-spaces diffeomorphic to \(\mathbb{R}^3\), Energy-momentum tensor on foliations, Height and area estimates for constant mean curvature graphs in \(\mathbb {E}(\kappa ,\tau )\)-spaces, A Bonnet theorem for submanifolds into rotational hypersurfaces, Spinorial representation of submanifolds in metric Lie groups, Higher order parallel surfaces in the Heisenberg group, Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds, Uniqueness of quasi-Einstein metrics on 3-dimensional homogeneous manifolds, On the Gauss curvature of compact surfaces in homogeneous 3-manifolds, Associated family of \(G\)-structure preserving minimal immersions in semi-Riemannian manifolds, Maximal surfaces in Lorentzian Heisenberg space, Hypersurfaces of \(\mathrm{Spin}^{c}\) manifolds and Lawson type correspondence, A complete classification of parallel surfaces in three-dimensional homogeneous spaces, New examples of constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times \mathbb R\), Rigidity of convex surfaces in the homogeneous spaces, On complete constant mean curvature vertical multigraphs in \(\mathbb E(\kappa,\tau)\), Equivariant Willmore surfaces in conformal homogeneous three spaces, Constant angle surfaces in the Heisenberg group, Spinorial characterizations of surfaces into three-dimensional homogeneous manifolds, Surfaces of \(M_k^2\times \mathbb R \) invariant under a one-parameter group of isometries, Isometric immersions into \(\mathbb{S}^m \times \mathbb{R}\) and \(\mathbb{H}^m \times \mathbb{R}\) with high codimensions, Minimal graphs in \(\widetilde{\mathrm{PSL}_2(\mathbb R)}\) over unbounded domains, Rigidity of cmc surfaces in the Berger sphere, The Gauss map of surfaces in \(\widetilde{\mathrm {PSL}}_2(\mathbb R)\), The half space property for cmc 1/2 graphs in \(\mathbb {E}(-1,\tau )\), On the first stability eigenvalue of constant mean curvature surfaces into homogeneous 3-manifolds, A fundamental theorem for submanifolds in semi-Riemannian warped products, Rotationally invariant constant mean curvature surfaces in homogeneous 3-manifolds, An extension of Ruh-Vilms’ theorem to hypersurfaces in symmetric spaces and some applications, Biharmonic constant mean curvature surfaces in Killing submersions, A Simons type integral inequality for closed submanifolds in the product space \(\mathbb{S}^n\times\mathbb{R}\), The classification of totally umbilical surfaces in homogeneous 3-manifolds, Rigidity of surfaces with constant extrinsic curvature in Riemannian product spaces, Hypersurfaces with a parallel higher fundamental form, Classical Schwarz reflection principle for Jenkins-Serrin type minimal surfaces, The geometry of stable minimal surfaces in metric Lie groups, On the asymptotic plateau problem in \(\widetilde{\mathrm{SL}}_2 (\mathbb{R})\), Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space, A new approach on constant angle surfaces in the special linear group, A survey on minimal isometric immersions into \(\mathbb{R}^3\), \(\mathbb{S}^2\times \mathbb{R}\) and \(\mathbb{H}^2\times \mathbb{R} \), Magnetic curves in Sasakian manifolds, Killing graphs with prescribed mean curvature and Riemannian submersions, Compact minimal surfaces in the Berger spheres, Characterization of hypersurfaces in four-dimensional product spaces via two different \(\text{Spin}^{\text{c}}\) structures, The Abresch–Rosenberg shape operator and applications, Graphs and multi-graphs in homogeneous 3-manifolds with isometry groups of dimension 4, Surfaces with parallel mean curvature vector in $\mathbb{S}^{2}×\mathbb{S}^{2}$ and $\mathbb{H}^{2}×\mathbb{H}^{2}$, On the asymptotic plateau problem for area minimizing surfaces in \({\mathbb{E}}(-1,\tau )\), On rigidity phenomena of compact surfaces in homogeneous $3$-manifolds, Isoparametric surfaces in $E(\kappa,\tau)$-spaces, CMC spheres in the Heisenberg group, Constant mean curvature \(k\)-noids in homogeneous manifolds, Properly immersed minimal surfaces in a slab of \(\mathbb H\times\mathbb R\), \(\mathbb H\) the hyperbolic plane, A new characterization of the Berger sphere in complex projective space, Minimal surfaces with non-trivial geometry in the three-dimensional Heisenberg group, Invariants of Riemannian curves in dimensions 2 and 3, Extremal curves of the total curvature in homogeneous 3-spaces, Spinorial representation of surfaces in Lorentzian homogeneous spaces of dimension 3
