On 3-dimensional Riemannian manifolds with prescribed Ricci eigenvalues
Stana Nikcevic. Universidade de Belgrado
Luns 1 de decembro de 2008 ás 17 horas na aula 9.
- For three-dimensional Riemannian manifold (M, g) we have the following simple criterion: (M, g) is curvature homogeneous if and only if all principle Ricci curvatures of (M, g) are constant. Thus the problem of classifying all three-dimensional Riemannian manifold with prescribed three constant Ricci eigenvalues is of considerable interest. For every prescribed constant r1, r2, r3 there exist a three-dimensional Riemannian manifold with contant Ricci eigenvalues r1, r2, r3. If the numbers ri are not equal, then there always exists a corresponding Riemannian manifold (M, g) which is not locally homogeneous. On the other hand, it is not always possible to find a locally homogeneous Riemannian 3-manifold with arbitrary prescribed Ricci eigenvalues. We determine precisely the range of all triplets from R3 which can occur as corresponding Ricci eigenvalues of locally homogeneous Riemannian 3-manifolds. This is the join work with Oldrich Kowalski.