Isotopic lifting on differential geometries

• Ruggero María Santilli Istituto per la Ricerca di Base Castello Principe Pignatelli-Italia

Abstract

In the first paper of this series we have introduced the isotopies of the differential calculus and of Newton's equations of motion. In the second paper we used these results to construct the isotopies of analytic and quantum mechanics. In th1s third paper we apply the preceding results for the construction of the isotopies of conventional differential geometries, such as the symplectic and Riemannian geometrites. The primary motivation is that, in their conventional formulation, these geometrites are local-differential. As such, the are only valid for the exterior dynamical problem ofpoint-l1ke test bodies moving in the homogeneous and isotropic vacuum. The isotopic geometrites result instead to be valid for the interior dynam1cal problem of extended and deformable test bodies moving With1n inhomogeneous and isotropic physical media With conventional local-differential and variattonally self-adjoint as well as nonlocal-integral and vartationally nonselfadjoint resistlve forces. In th1s papa we show that the isotopic geometrites preserve all original axioms to such and extent that they coincide at the abstract level With the conventional geometrites.