Isometry group

Mean curvature

Linguistics

Philosophy

Curvature

SPHERES

Ambient space

Economics

Computer science

Constant curvature

Physics

Homogeneous

Mathematics

Astronomy

Mathematical analysis

Operations management

Geometry

Combinatorics

Programming language

Metric (unit)

Isometry (Riemannian geometry)

Space (punctuation)

Constant (computer programming)

Journal of Differential Geometry

We give a complete classification of the immersed constant mean curvature spheres in a three-sphere with an arbitrary homogeneous metric, by proving that for each $H \in \mathbb{R}$, there exists a constant mean curvature $H$ sphere in the space that is unique up to an ambient isometry.

Constant mean curvature spheres in homogeneous three-spheres