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G2: Killing-tensors

Principal Investigators: Matveev, Meinel, Wipf

Killing- and Killing-Yano-tensors correspond to conservative quantities that are polynomial in the variable of velocity. Since Jacobi it is known that such conservative quantities are useful for the qualitative and quantitative description of geodesics. For example the existence of Killing-tensors of rank 2 allows us to find a coordinate system in which the geodesic equations in the Kerr-metric are decoupled ordinary differential equations of one variable. The goal of the project is to describe (locally) all Einstein metrics admitting sufficiently many Killing- and Killing-Yano-tensors, and to construct curvature invariants that vanish if and only if a given Einstein metric admits a Killing-tensor.

further information (german)


Examples of Ph.D. topics


  1. Killing-Tensoren für stationäre und axialsymmetrische Vakuum-Gravitationsfelder
  2. Existenz und Konstuktionsmöglichkeit einer Raumzeit mit gegebenem projektiven Zusammenhang
  3. Killing-Tensoren 2. Stufe und Quanten-Integrabilität
  4. Erhaltungsgrößen für Systeme mit Spin auf kompakten Mannigfaltigkeiten


Publications


V. S. Matveev, S. Rosemann
Two Remarks on $PQ^{\epsilon}$-projectivity of Riemannian metrics
arXiv:1108.2965v1 [math.DG], Aug 2011



V. S. Matveev, S. Rosemann
Proof of the Yano-Obata conjecture for holomorph-projective transformations
arXiv:1103.5613 [math.DG], Mar 2011



A. Fedorova, S. Rosemann
The Tanno-Theorem for K\"ahlerian metrics with arbitrary signature
Differential Geometry and its Applications 29 (S1), 71-79 (2011), arXiv:1012.1181v1 [math.DG], Dec 2010



A. Fedorova, V. Kiosak, V. S. Matveev, S. Rosemann
The only K\"ahler manifold with degree of mobility $\geq 3$ is $(CP(n),g_{Fubini-Study})$
arXiv:1009.5530v2 [math.DG], Sep 2010