## About the project

This project **finished last May 31, 2023**. For the new research project see CMC

This project focuses on the study of constant mean curvature surfaces in homogeneous Riemannian manifolds of dimension three and four. The main goal of this research proposal is to delve into the role played by the mean curvature in the properties of a surface from different points of view. The posed problems deal with the construction and characterization of examples, as well as the study of global geometric properties related to open problems that have guided the research in this area in the last decades.

The main goals of CMC are the following:

- Move forward in our understanding of minimal and H-surfaces in the homogeneous Riemannian 3-manifolds Ε(κ, τ) by means of construction and characterization of examples and the study of admissible topological types.
- Develop the theory of parallel mean curvature surfaces in Thurston 4-dimensional geometries in order to get classification results about them.