space metric tensor

Aim. Solving the problem associated in using GNSS monitoring data in the ITRS to evaluate deformation of fields of the Earth in terms of elimination of invariance loss errors. Methodology and results. The problem is considered in the context of the geophysical nature of the ITRS in conjunction with the global deformation field of the Earth. The attention is focused on the consequences of deformation of the ITRS system, which manifests itself as invariance loss effects in the interpretation of deformation fields.

Aim. The aim is to solve the problem of evaluating the Earth’s topographic surface deformations using
projective differential geometry methods as an expression of the space metric tensor and the group of main linear
deformation parameters in the spatial geocentric coordinate system. Methodology. Solving the problem is based
on using the homeomorphism transformation (mapping) properties of the three-dimensional continuous and
closed domains of the space with the hypothesis that this transformation has a geophysical origin and was caused

Aim. The aim is this research is the evaluation of the Earth’s rigid rotation as a component of global deformation fields in interconnection with angular distortions of the geocentric spatial coordinate system. Methodology. Solutions will be achieved by methods of  projective differential (metric) geometry based on the differential presentation of transformations of Riemannian space images in the form of its complicated diffeomorphic manifolds.