Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/119419
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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 1618-1891 |
Statement of Responsibility: | 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 |
Published version: | http://dx.doi.org/10.1007/s10231-018-0775-3 |
Appears in Collections: | Aurora harvest 3 Mathematical Sciences publications |
Files in This Item:
File | Description | Size | Format | |
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hdl_119419.pdf | Submitted version | 721.53 kB | Adobe PDF | View/Open |
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