Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 24, No. 1, pp. 33-49 (2008)

A special nonlinear connection in second order geometry

N. Brinzei

Transilvania University

Abstract: We show that, for mechanical system with external forces, the equations of deviations of solution curves of the corresponding Lagrange equations, determine a nonlinear connection on the second order tangent bundle. In particular, Jacobi equations in Finsler and Riemann spaces determine such a nonlinear connection.

Keywords: nonlinear connection, 2-tangent bundle, Finsler space, Jacobi equations

Classification (MSC2000): 53B40; 70H50

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