On the total space of a G−complex vector bundle E is defined the gauge transformations. A gauge complex invariant Lagrangian determines a special complex nonlinear connection for which the associated Chern-Lagrange and Bott complex connections are gauge invariant. The complex field equations are determined with respect to these associated gauge complex connections. By complex Legendre transform...

Recently, a max-plus dual space fundamental solution for a class of difference Riccati equations (DREs) has been developed. This fundamental solution is represented in terms of the kernel of a specific max-plus linear operator that plays the role of the dynamic programming evolution operator in a max-plus dual space. In order to fully understand connections between this dual space fundamental s...

We consider the problem of a self-interacting scalar field nonminimally coupled to the three-dimensional BTZ metric such that its energymomentum tensor evaluated on the BTZ metric vanishes. We prove that this system is equivalent to a self-dual system composed by a set of two first-order equations. The self-dual point is achieved by fixing one of the coupling constant of the potential in terms ...