Curvature and torsion pseudotensors of coaffine connection in tangent bundle of hypercentred planes manifold

Abstract

The hypercentered planes family, whose dimension coincides with dimension of generating plane, is considered in the projective space. Two principal fiber bundles arise over it. Typical fiber for one of them is the stationarity subgroup for hypercentered plane, for other — the linear group operating in each tangent space to the manifold. The latter bundle is called the principal bundle of linear coframes. The structural forms of two bundles are related by equations. It is proved that hypercentered planes family is a holonomic smooth manifold. In the principal bundle of linear coframes the coaffine connection is given. From the differential equations it follows that the coaffine connec­tion object forms quasipseudotensor. It is proved that the curvature and torsion objects for the coaffine connection in the linear coframes bundle form pseudotensors.

Keywords

• projective space
• hypercentered planes family
• coaffine connection
• curvature pseudotensor
• torsion pseudotensor