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Type: Journal article
Title: Invariant prolongation of the Killing tensor equation
Author: Gover, A.
Leistner, T.
Citation: Annali di Matematica Pura ed Applicata, 2019; 198(1):307-334
Publisher: Springer
Issue Date: 2019
ISSN: 0373-3114
Statement of
A. Rod Gover, Thomas Leistner
Abstract: The Killing tensor equation is a first-order differential equation on symmetric covariant tensors that generalises to higher rank the usual Killing vector equation on Riemannian manifolds. We view this more generally as an equation on any manifold equipped with an affine connection, and in this setting derive its prolongation to a linear connection. This connection has the property that parallel sections are in 1–1 correspondence with solutions of the Killing equation. Moreover, this connection is projectively invariant and is derived entirely using the projectively invariant tractor calculus which reveals also further invariant structures linked to the prolongation.
Keywords: Integrability; hidden symmetries; projective differential geometry; Riemannian manifolds; Affine manifolds
Rights: © Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2018
DOI: 10.1007/s10231-018-0775-3
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