Codazzi Tensors and the Quasi-Statistical Structure Associated with Affine Connections on Three-Dimensional Lorentzian Lie Groups

In this paper, we classify three-dimensional Lorentzian Lie groups on which Ricci tensors associated with Bott connections, canonical connections and Kobayashi–Nomizu connections are Codazzi tensors associated with these connections. We also classify three-dimensional Lorentzian Lie groups with the quasi-statistical structure associated with Bott connections, canonical connections and Kobayashi–Nomizu connections.

Generalized Affine Connections Associated with the Space of Centered Planes

Our purpose is to study a space Π of centered m-planes in n-projective space. Generalized fiberings (with semi-gluing) are investigated. Planar and normal affine connections associated with the space Π are set in the generalized fiberings. Fields of these affine connection objects define torsion and curvature tensors. The canonical cases of planar and normal generalized affine connections are considered.

Almost Paracontact Almost Paracomplex Riemannian Manifolds with a Pair of Associated Schouten–van Kampen Connections

Two correlated Schouten–van Kampen affine connections on an almost paracontact almost paracomplex Riemannian manifold are introduced and investigated. The considered manifolds are characterized by virtue of the presented non-symmetric connections. Curvature properties of the studied connections are obtained. A family of examples on a Lie group are given in confirmation of the obtained results.

Affine connections on singular warped products

In this paper, we introduce semi-symmetric metric Koszul forms and semi-symmetric non-metric Koszul forms on singular semi-Riemannian manifolds. Semi-symmetric metric Koszul forms and semi-symmetric non-metric Koszul forms and their curvature of semi-regular warped products are expressed in terms of those of the factor manifolds. We also introduce Koszul forms associated with the almost product structure on singular almost product semi-Riemannian manifolds. Koszul forms associated with the almost product structure and their curvature of semi-regular almost product warped products are expressed in terms of those of the factor manifolds. Furthermore, we generalize the results in [O. Stoica, The geometry of warped product singularities, Int. J. Geom. Methods Mod. Phys. 14(2) (2017) 1750024, arXiv:1105.3404 .] to singular multiply warped products.

Canonical Almost Geodesic Mappings of the First Type of Spaces with Affine Connections onto Generalized m-Ricci-Symmetric Spaces

In the paper we consider almost geodesic mappings of the first type of spaces with affine connections onto generalized 2-Ricci-symmetric spaces, generalized 3-Ricci-symmetric spaces, and generalized m-Ricci-symmetric spaces. In either case the main equations for the mappings are obtained as a closed system of linear differential equations of Cauchy type in the covariant derivatives. The obtained results extend an amount of research produced by N.S. Sinyukov, V.E. Berezovski, J. Mikeš.

Completeness in affine and statistical geometry

We begin the study of completeness of affine connections, especially those on statistical manifolds or on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.

Almost geodesic mappings of type π1* of spaces with affine connection

We consider almost geodesic mappings π1* of spaces with affine connections. This mappings are a special case of first type almost geodesic mappings. We have found the objects which are invariants of the mappings π1*. The fundamental equations of these mappings are in Cauchy form. We study π1* mappings of constant curvature spaces.

Canonical Almost Geodesic Mappings of the First Type of Spaces with Affine Connection Onto Generalized 2-Ricci-Symmetric Spaces

In the paper we consider almost geodesic mappings of the first type of spaces with affine connections onto generalized 2-Ricci-symmetric spaces. The main equations for the mappings are obtained as a closed system of linear differential equations of Cauchy type in the covariant derivatives. The obtained result extends an amount of research produced by Sinyukov, Berezovski and Mike\v{s}.