Killing and Conformal Killing tensors

Abstract

We introduce an appropriate formalism in order to study conformal Killing (symmetric) tensors on Riemannian manifolds. We reprove in a simple way some known results in the field and obtain several new results, like the classification of conformal Killing $2$-tensors on Riemannian products of compact manifolds, Weitzenböck formulas leading to non-existence results, and construct various examples of manifolds with conformal Killing tensors.

29 pages; the statement and the proof of Theorem 5.1 have been corrected

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Cited by in corpus (21)

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• Fried conjecture in small dimensions
• Rational first integrals of geodesic equations and generalised hidden symmetries
• Sectional curvature and Weitzenböck formulae
• Symmetric Killing tensors on nilmanifolds
• Killing tensors on tori
• Resonances for Symmetric Tensors on Asymptotically Hyperbolic Spaces
• Quadratic Killing structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians
• Killing sections and sigma models with Lie algebroid targets
• On the ergodicity of the frame flow on even-dimensional manifolds
• Generalized vector cross products and Killing forms on negatively curved manifolds
• A special class of symmetric Killing 2-tensors
• Jacobi relations on naturally reductive homogeneous spaces
• Correspondence between Pestov and Weitzenböck identities
• Curvature operators and rational cobordism
• Linear Instability of Sasaki Einstein and nearly parallel ${\mathrm{G}}_2$ manifolds
• Killing tensors on reducible spaces
• Geometry in the large of the kernel of Lichnerowicz Laplacians and its applications
• First integrals on step-two and step-three nilpotent Lie groups
• Asymptotically Euclidean metrics without conjugate points are flat
• The spinor and tensor fields with higher spin on spaces of constant curvature