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An elementary differential analysis of the covariant law of particleacceleration in gravitation field of General Theory of Relativity (GTR)discovers that, conventional certification of the geodesics is not compatiblewith the existence of the Riemann-Christoffel curvature tensor (RCT). We showthat, a resolution of this crisis consists of a natural extension of theCristoffels in the dynamic law to general connectedness form including atriadic asymmetric tensor (named the moderator). The correspondent Riemanntensor form, unavoidably annihilating by certification of the moderategeodesics, gives birth to torsion (skew-symmetric part of the moderator) andthe gravitensor (the even-symmetric part); both arrive as a functional of theRCT and become an indispensable integral part of structure of the gravitationalinteraction. The equivalence principle still actual while being enriched in thecontent. The Einstein-Hilbert law of the metric to matter connection remainsunchanged at the produced correction of the gravitational dynamics. We payattention to possible implication of the torsion in the elementaryinteractions.

To the Issue of the Geodesics and Torsion in Riemannian Geometry and Theory of the Gravitation