Degree of mobility for metrics of lorentzian signature and parallel (0,2)-tensor fields on cone manifolds

Abstract

Degree of mobility of a (pseudo-Riemannian) metric is the dimension of the space of metrics geodesically equivalent to it. We describe all possible values of the degree of mobility on a simply connected n-dimensional manifold of lorentz signature. As an application we calculate all possible differences between the dimension of the projective and the isometry groups. One of the main new technical results in the proof is the description of all parallel symmetric (0,2)-tensor fields on cone manifolds of signature $(n-1,2).

30 pages, 1 figure

References in corpus (4)

• Invariant characterization of Liouville metrics and polynomial integrals
• Metrisability of three-dimensional projective structures
• The algebra of parallel endomorphisms of a germ of pseudo-Riemannian metric
• On parallel and symmetric 2-tensorfields on cones over pseudo-Riemannian manifolds

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• (Super-)integrable systems associated to 2-dimensional projective connections with one projective symmetry
• A special class of symmetric Killing 2-tensors
• The degree of mobility of Einstein metrics