Killing symmetries of generalized Minkowski spaces. 3-Space-time translations in four dimensions

In this paper, we continue the study of the Killing symmetries of a N-dimensional generalized Minkowski space, i.e. a space endowed with a (in general non-diagonal) metric tensor, whose coefficients do depend on a set of non-metrical coodinates. We discuss here the translations in such spaces, by confining ourselves (without loss of generality) to the four-dimensional case. In particular, the results obtained are specialized to the case of a ‘‘deformed’’ Minkowski space $\widetilde{M_4}$ (i.e. a pseudoeuclidean space with metric coefficients depending on energy).