ON THE SPACE OF 3--DIMENSIONAL HOMOGENEOUS
RIEMANNIAN MANIFOLDS

Hans - J\"urgen Schmidt

1991 Math. Subject Classification: 53B20.

Key words: Homogeneous Riemannian manifolds, local classification in $d=3$.

Abstract: We answer the following question: Let $\lambda$,
$\mu$, $\nu$ be arbitrary  real numbers. Does there exist a
3--dimensional homogeneous Riemannian manifold
whose eigenvalues of the Ricci tensor are just
$\lambda$, $\mu$, and  $\nu$?