  We recall that the Minkowskian geometry possesses basic units of space and
time which are invariant under the Poincar\'{e} symmetry. We then show that, by
comparison, the Riemannian geometry possesses space-time units which are not
invariant under the symmetries of the Riemannian line element, thus causing
evident physical ambiguities. We therefore introduce a novel formulation of
general relativity in the isominkowskian geometry which is an axiom-preserving
lifting of the conventional Minkowskian geometry but which nevertheless admits
all possible Riemannian metrics thanks to a (positive-definite) $4 \times 4$
generalization of the basic unit. We construct the universal symmetry of the
isominkowskian line elements called isopoincar\'{e} symmetry}, prove that it is
locally isomorphic to the conventional Poincar\'{e} symmetry, and show that, in
this way, conventional Riemannian metrics and related field equations can be
expressed with respect to invariant generalized units of space and time. We
then show that the isominkowskian geometry and related isopoincar\'{e} symmetry
permit: I) A classical geometric unification of the general and special
relativities for matter into a formulation called isospecial relativity in
which the former occurs for generalized units while admitting the latter as a
particular case for conventional units; II) A novel operator formulation of
gravity for matter based on the abstract axioms of relativistic quantum
mechanics, thus showing hope for a possible resolution of the ambiguities in
current theories of quantum gravity; and III) A novel classical and operator
formulation of antimatter which is an antiautomorphic image of the preceding
formulations for matter constructed via a map called isoduality. The
