This survey paper investigates, from a purely geometric point of view, Daniel's isometric
conjugation between minimal and constant mean curvature surfaces immersed in …

This is a survey on the global theory of constant mean curvature surfaces in Riemannian
homogeneous 3-manifolds. These ambient 3-manifolds include the eight canonical Thurston …

We provide an explicit classification of the following four families of surfaces in any
homogeneous 3-manifold with 4-dimensional isometry group: isoparametric surfaces …

The classical Bonnet problem is to classify all immersions f: M 2→ R 3 into Euclidean three-
space that are not determined, up to a rigid motion, by their induced metric and mean …

For a given simply connected Riemannian surface Σ, we relate the problem of finding
minimal isometric immersions of Σ into 𝕊2× ℝ or ℍ2× ℝ to a system of two partial differential …

Some classification results for closed surfaces in Berger spheres are presented. On the one
hand, a Willmore functional for isometrically immersed surfaces into an homogeneous space …

We define a Gauss map for surfaces in the universal cover of the Lie group PSL _2 (R) PSL
2 (R) endowed with a left-invariant Riemannian metric having a 4 4-dimensional isometry …

Hopf's theorem has been recently extended to compact genus zero surfaces with constant
mean curvature H in a product space, where is a surface with constant Gaussian curvature …

We study the moduli space of congruence classes of isometric surfaces with the same mean
curvature in 4-dimensional space forms. Having the same mean curvature means that there …

In this note we consider Lagrangian Bonnet problem for Lagrangian surfaces in complex
space forms. We first give a Bonnet type theorem for conformal Lagrangian surfaces in …