Second Order Lagrange Spaces

Abstract

The notion of second order Lagrange space is a natural extension of the notion of Lagrange space L n = (M, L) introduced in the §6, Ch.1. The second order Lagrange space is defined as a pair L (2)n = (M, L) where M is a real n-dimensional manifold and L is a differentiable regular Lagrangian of second order, whose fundamental tensor field has a constant signature on Ẽ.