On a connection with a torsion non-tensor and a curvature non-tensor

Abstract

This paper relates to differential geometry, and the research technique is based on G. F. Laptev’s method of extensions and envelopments, which generalizes E. Cartan's method of moving frame and exterior forms. A manifold is studied, the structure equations and derivational for­mu­las of which are built using the deformations of the exterior and ordinary differentials. The manifold in question is a deformation of an ordinary smooth manifold. The bundles of non-symmetrical coframes and frames of the second order on this manifold are examined and an affine con­nec­tion is given. It is proved that the curvature and torsion of this connection are not tensors. A canonical connection is built. It is shown that the cano­ni­cal connectionis flat and non-symmetrical.

Keywords

• differential perturbation
• second order tangent space
• non-symmetrical second order frames and coframes
• torsion and curvature objects
• flat and non-symmetrical connection