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Order reduction of the Euler-Lagrange equations of higher order invariant variational problems on frame bundles

Ján Brajerčík (2011)

Czechoslovak Mathematical Journal

Let μ : F X X be a principal bundle of frames with the structure group Gl n ( ) . It is shown that the variational problem, defined by Gl n ( ) -invariant Lagrangian on J r F X , can be equivalently studied on the associated space of connections with some compatibility condition, which gives us order reduction of the corresponding Euler-Lagrange equations.

Osculating curves in 4-dimensional semi-Euclidean space with index 2

Kazim İlarslan, Nihal Kiliç, Hatice Altin Erdem (2017)

Open Mathematics

In this paper, we give the necessary and sufficient conditions for non-null curves with non-null normals in 4-dimensional Semi-Euclidian space with indeks 2 to be osculating curves. Also we give some examples of non-null osculating curves in [...] E24 𝔼 2 4 .

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