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Displaying similar documents to “Higher order almost tangent geometry and non-autonomous Lagrangian dynamics”

Sprays and homogeneous connections on 𝐑 × 𝑇𝑀

Alexandr Vondra (1992)

Archivum Mathematicum

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The homogeneity properties of two different families of geometric objects playing a crutial role in the non-autonomous first-order dynamics - semisprays and dynamical connections on R × T M - are studied. A natural correspondence between sprays and a special class of homogeneous connections is presented.

On naturality of the Helmholtz operator

Włodzimierz M. Mikulski (2005)

Archivum Mathematicum

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We deduce that all natural operators of the type of the Helmholtz map from the variational calculus in fibered manifolds are the constant multiples of the Helmholtz operator.