Study of the generalized Lagrange space ${GL^{2n}(M,g_{ij}(x,y^{(1)},y^{(2)})=e^{2\sigma(x,y^{(1)}, y^{(2)})} \gamma_{ij} (x))}$

Marius Păun

The purpose of this paper is to study the fundamental equations for a generalized Lagrange space of order 2. The metric tensor $g_{ij}(x)=e^{2\sigma(x)}\gamma_{ij}(x)$ was introduced on the base manifold by Watanabe, Ykeda S. and Ykeda F. Einstein and Maxwell equations for the space $GL^n(M,g_{ij}(x,y)=e^{2\sigma(x,y)}\gamma_{ij}(x))$ were studied by R. Miron and R. Tavakol.