Isometric embedding for homogeneous compact 3-manifolds

Abstract

The anisotropic homogeneous ℙ³ is isometrically globally embedded into a nine-dimensional Euclidean or pseudo-Euclidean space. In a special case the Euclidean space is six-dimensional. The space-sections of the anti-Mach metric appear as a submanifold of theE ⁹. We obtain also the isometric embedding ofSO(3) with its natural Killing metric.