Finslerian metric functions over the product R × M and their potential applications

A broad class of Finslerian metric functions possessing a remarkable property that the associated indicatrices are constant-curvature spaces has been found in [1] when studying the GF-spaces which generalize the Riemannian concept of the static and spherically symmetric space in a quite consistent Finslerian way. In the present paper, we indicate simple explicit transformations which turn the associated indicatrix metric tensors into a canonical constantcurvature form. The transformations can further be extended to operate over the tangent space. The resultant transformations are remarkable in showing that the Finslerian metric functions under study are nonlinear transforms of simple quasi-Euclidean metric functions. The invariance properties of the Finslerian metric functions are studied and various possible directions of Finslerian physical applications are discussed.