Tilbake til søkeresultatene

IS-DAAD-Forskerutveksl. Norge-Tyskland

Differential-Geometric Structures: Invariants and Integrals

Tildelt: kr 71 608

The Project aims to unite forces of the Norwegian and German research groups and to focus on several important research problems of common interest described below. 1. Computation of number and form of differential invariants characterizing Riemannian and pseudo-Riemannian spaces admitting Killing vectors and Killing tensors. Both groups have an active interest in this problem and some partial results. 2. Recognition and classification of metrics with a simply or multiply transitive local group of isometries, in submaximally symmetric cases and in low dimensions. For Kundt metrics, indistinguishable by scalar curvature invariants, address their integrability via first and second order integrals. Both group have sufficient expertise required for these tasks. 3. Generalization, in particular, to parabolic geometries, like conformal and projective. Investigation which differential invariants are responsible for existence of normal solutions to BGG-type invariant differential operators, estimation of the number and order of such invariants. Both sides have own approaches, which are complementary, and so a joint study should be very prolific. 4. Investigation of projective invariance and integrability for Finsler metrics. The Jena partners have a considerable knowledge in this area, to be shared with the Norwegian group. In response the Lie representation-theoretic methods, known to Tromsø group, will be applied to the problems in Finsler geometry. In particular, we are going to work on Finsler metrics with sub maximal symmetry dimension. 5. Extensions of the results to low regularity problems. Applications to recognition of symmetric metrics via stable joint invariant techniques. The two groups have had preliminary contacts and meetings, which give a definite hope to construct a fruitful dialog and lay a foundation for future collaborations.


IS-DAAD-Forskerutveksl. Norge-Tyskland