The Berwald-Moor metric in the tangent bundle of the second order 2005jbo | Gheorghe Atanasiu, Nicoleta Brinzei
As an application of the results of the first author obtained in the papers
\cite{1} and \cite{2}, the geometry of the second order tangent bundle $%
T^{2}M$ (or second order jet bundle $J_{0}^{2}M$) endowed with two special types of metrics compatible with the 2-contact structures is studied. The particularity of these two models is that the horizontal and the $v^{(1)}$-\ part of the metric are both given by the same Riemannian metric (respectively, its horizontal part is
Riemannian), while its $v^{(2)}$-part is given by the flag-Finsler Berwald-Moor metric (respectively, the $v^{(1)} $ and $v^{(2)}$- parts are given by the
flag-Finsler Berwald-Moor metric, \cite{Mangalia}).
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