Structure Equations, Permitted Movement of Relativistic Continuum and Sagnac’s, Erenfest’s and Bell’s Paradoxes

From obtained structure equations, restrictions on a space-time geometry for possible solutions of relativistic continua are studied. The Minkowski space proved to be “cramped” to describe the continuum if except for the medium motion equations one imposes rigidity and rotation conditions. The continuum is a basis of noninertial reference frames (NRF) where one studies different physical processes. For example, bases of simplest NRF are constructed: 1. Relativistic globally uniformly accelerated Born rigid NRF. 2. Relativistic Born rigid uniformly rotating reference frame (RF) without a horizon. 3. Rigid irrotational spherically symmetrical quasi-Einstein’s NRF. One can’t describe bases of these systems in the Minkowski space, the Riemannian space-time is needed. The space-time of these RF is not directly connected with the general relativity theory (GRT), though it imposes conditions on some solutions of the Einstein equations. A solution of the Sagnac’s, Erenfest’s and Bell’s paradoxes is proposed.