Hokkaido Mathematical Journal

Moving frames and conservation laws of a Lagrangian invariant under the Hyperbolic Rotation-Translation group


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Noether's First Theorem guarantees conservation laws provided that the Lagrangian is invariant under a Lie group action. In this paper, via the concept of Killing vector fields and the Minkowski metric, we first construct an important Lie group, known as Hyperbolic Rotation-Translation group. Then, according to Gonçalves and Mansfield's method, we obtain the invariantized Euler-Lagrange equations and the space of conservation laws in terms of vectors of invariants and the adjoint representation of a moving frame, for Lagrangians, which are invariant under Hyperbolic Rotation-Translation (or HRT) group action, in the case where the independent variables are not invariant.

Article information

Hokkaido Math. J., Volume 47, Number 3 (2018), 557-579.

First available in Project Euclid: 26 September 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L65: Conservation laws 58E30: Variational principles 70S10: Symmetries and conservation laws 53B30: Lorentz metrics, indefinite metrics 53C50: Lorentz manifolds, manifolds with indefinite metrics 58D19: Group actions and symmetry properties 43A65: Representations of groups, semigroups, etc. [See also 22A10, 22A20, 22Dxx, 22E45]

Conservation laws Moving frames Differential invariants Normalized differential invariants Syzygies Killing vector fields


MASOUDI, Yousef; NADJAFIKHAH, Mehdi. Moving frames and conservation laws of a Lagrangian invariant under the Hyperbolic Rotation-Translation group. Hokkaido Math. J. 47 (2018), no. 3, 557--579. doi:10.14492/hokmj/1537948831. https://projecteuclid.org/euclid.hokmj/1537948831

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