Geodesic Ricci-symmetric pseudo-Riemannian spaces

Abstract

We introduced special pseudo-Riemannian spaces, called geodesic A-symmetric spaces, into consideration. It is proven that there are no geodesic symmetric spaces and no geodesic Ricci symmetric spaces, which differ from spaces of constant curvature and Einstein spaces respectively. The research is carried out locally, by tensor methods, without any limitations imposed on a metric and a sign.

On geodesic mappings of symmetric pairs

“…Moreover, for example, Einstein spaces for n ą 4, quasi-Einstein spaces, and Ricci solitons admit non-trivial geodesic mappings only under certain restrictions on vectors of main equations [1,4,5,9,11,17,22]. Also four-dimensional Einstein spaces, symmetric spaces, geodesic symmetric spaces [3] admit non-trivial geodesic mappings if they are spaces of constant curvature.…”

On geodesic mappings of threesymmetric spaces

“…In the theory of geodesic mappings, the main results for these spaces were obtained by M. S. Sinyukov [13]. Later, it became clear that the question of covariant stability of not only the internal objects of pseudo-Riemannian spaces, but also of arbitrary tensors is of interest [3][4][5].…”

“…In the theory of geodesic mappings, the main results for these spaces were obtained by M. S. Sinyukov [13]. Later, it became clear that the question of covariant stability of not only the internal objects of pseudo-Riemannian spaces, but also of arbitrary tensors is of interest [3][4][5].In particular, to study the possibility of reducing the metric tensor to a special form [2]. Following the way of increasing the number of derivatives, M. S. Sinyukov came to the study of geodesic mappings of semisymmetric spaces.…”

Conformal recurrent Kӓhler spaces

“…The notion of tensor recurrence generalizes the notion of symmetry. Other ways of generalization proposed in [8,9,15,21] allow application in the theory of recurrence tensors in Kähler spaces.…”