A Curved Space-time with DISIMb(2) Local Relativistic Symmetry and Local Gauge Invariance of Its Finslerian Metric: A Recent Study

It is shown that the equations of motion of test bodies as well as the observable quantities of proper time and 3-space distances are invariant under the local gauge transformations of the fields that determine invariant Finslerian metric of a curved partially anisotropic space-time. The principle of the corresponding local gauge invariance makes it possible to effectively attack the problem of constructing the field Lagrangian and deriving the field equations of the Finslerian general relativity.