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Published in:
Contact Geometry, Measurement, and Thermodynamics Read chapter Read first chapter

2019 | OriginalPaper | Chapter

10. Integrability of Geodesics of Totally Geodesic Metrics

Authors : Radosław A. Kycia, Maria Ułan

Published in: Nonlinear PDEs, Their Geometry, and Applications

Publisher: Springer International Publishing

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Abstract

Analysis of the geodesics in the space of the signature (1, 3) that splits in two-dimensional distributions resulting from the Weyl tensor eigenspaces—hyperbolic and elliptic ones—described in [V.V. Lychagin, V. Yumaguzhin, Differential invariants and exact solutions of the Einstein equations, Anal. Math. Phys. 1664-235X 1–9 (2016)] is presented. The cases when geodesic equations are integrable are identified. A similar analysis is performed for the model coupled to electromagnetism described in [V.V. Lychagin, V. Yumaguzhi, Differential invariants and exact solutions of the Einstein–Maxwell equation, Anal. Math. Phys. 1, 19–29, (2017)].

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previous chapter Weak Inverse Problem of Calculus of Variations for Geodesic Mappings and Relation to Harmonic Maps
Footnotes
1
RK would like to thank Igor Khavkine for discussion on this subject and suggestions of the outline of the proof.
 
2
All calculations for this section are available as Maple files on: https://​github.​com/​rkycia/​GeodesicsIntegra​bility.
 
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Metadata
Title
Integrability of Geodesics of Totally Geodesic Metrics
Authors
Radosław A. Kycia
Maria Ułan
Copyright Year
2019
Book
Nonlinear PDEs, Their Geometry, and Applications

Print ISBN: 978-3-030-17030-1

Electronic ISBN: 978-3-030-17031-8

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-17031-8_10

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