Totally umbilic surfaces in homogeneous 3-manifolds
Rabah Souam, Eric Toubiana
Abstract
We discuss existence and classification of totally umbilic surfaces in the model geometries of Thurston and the Berger spheres. We classify such surfaces in H2 × R, S2 × R and the Sol group. We prove nonexistence in the Berger spheres and in the remaining model geometries other than the space forms.
Create a lesson
Related papers
Scalar curvature on Kähler blow-ups and systolic inequalities
Zehao Sha, Jian Wang
Strict Stability and Strict Minimality of Regular Area-Minimizing Hypercones: A Quantitative Characterization
Gongping Niu
Sharp partial regularity of Hamiltonian stationary and special Lagrangian graphs
Arunima Bhattacharya, Gerard Orriols, Anna Skorobogatova
Torus actions, almost non-negative curvature and fundamental groups
Michael Wiemeler
Optimal Transport and the ABP Method in Higher Codimension
Bang-Xian Han, Zhe-Feng Xu
An isoperimetric characterization of a new ADM-like mass for C0-asymptotically flat manifolds
Luca Benatti, Mattia Fogagnolo