-Планарные преобразования пространств аффинной связности
Conformally geodesic mappings satisfying a certain initial condition
In this paper we study conformally geodesic mappings between pseudo-Riemannian manifolds and , i.e. mappings satisfying , where are conformal mappings and is a geodesic mapping. Suppose that the initial condition is satisfied at a point and that at this point the conformal Weyl tensor does not vanish. We prove that then is necessarily conformal.
On special almost geodesic mappings of type of spaces with affine connection
N. S. Sinyukov [5] introduced the concept of an of a space with an affine connection without torsion onto and found three types: , and . The authors of [1] proved completness of that classification for .By definition, special types of mappings are characterized by equations where is the deformation tensor of affine connections of the spaces and .In this paper geometric objects which preserve these mappings are found and also closed classes of such spaces are described.
On tensor fields semiconjugated with torse-forming vector fields
The paper deals with tensor fields which are semiconjugated with torse-forming vector fields. The existence results for semitorse-forming vector fields and for convergent vector fields are proved.
On a classification of almost geodesic mappings of affine connection spaces
Shells of monotone curves
We determine in the form of curves corresponding to strictly monotone functions as well as the components of affine connections for which any image of under a compact-free group of affinities containing the translation group is a geodesic with respect to . Special attention is paid to the case that contains many dilatations or that is a curve in . If is a curve in and is the translation group then we calculate not only the components of the curvature and the Weyl tensor but...
On holomorphically projective mappings from manifolds with equiaffine connection onto Kähler manifolds
In this paper we study fundamental equations of holomorphically projective mappings from manifolds with equiaffine connection onto (pseudo-) Kähler manifolds with respect to the smoothness class of connection and metrics. We show that holomorphically projective mappings preserve the smoothness class of connections and metrics.
On -planar mappings of (pseudo-) Riemannian manifolds
We study special -planar mappings between two -dimensional (pseudo-) Riemannian manifolds. In 2003 Topalov introduced -projectivity of Riemannian metrics, . Later these mappings were studied by Matveev and Rosemann. They found that for they are projective. We show that -projective equivalence corresponds to a special case of -planar mapping studied by Mikeš and Sinyukov (1983) and -planar mappings (Mikeš, 1994), with . Moreover, the tensor is derived from the tensor and the non-zero...
Equipping distributions for linear distribution
In this paper there are discussed the three-component distributions of affine space . Functions , which are introduced in the neighborhood of the second order, determine the normal of the first kind of -distribution in every center of -distribution. There are discussed too normals and quasi-tensor of the second order . In the same way bunches of the projective normals of the first kind of the -distributions were determined in the differential neighborhood of the second and third order.
On -planar mappings of affine-connection spaces with infinite dimension
On scalar and total scalar curvatures of Riemann-Cartan manifolds
The Projectivization of Conformal Models of Fibrations Determined by the Algebra of Quaternions
Our aim is to study the principal bundles determined by the algebra of quaternions in the projective model. The projectivization of the conformal model of the Hopf fibration is considered as example.
On geodesic mappings preserving the Einstein tensor
In this paper there are discussed the geodesic mappings which preserved the Einstein tensor. We proved that the tensor of concircular curvature is invariant under Einstein tensor-preserving geodesic mappings.
On Almost Generalized Weakly Symmetric Kenmotsu Manifolds
This paper aims to introduce the notions of an almost generalized weakly symmetric Kenmotsu manifolds and an almost generalized weakly Ricci-symmetric Kenmotsu manifolds. The existence of an almost generalized weakly symmetric Kenmotsu manifold is ensured by a non-trivial example.
On holomorphically projective mappings from equiaffine generally recurrent spaces onto Kählerian spaces
In this paper we consider holomorphically projective mappings from the special generally recurrent equiaffine spaces onto (pseudo-) Kählerian spaces . We proved that these spaces do not admit nontrivial holomorphically projective mappings onto . These results are a generalization of results by T. Sakaguchi, J. Mikeš and V. V. Domashev, which were done for holomorphically projective mappings of symmetric, recurrent and semisymmetric Kählerian spaces.
From infinitesimal harmonic transformations to Ricci solitons
The concept of the Ricci soliton was introduced by R. S. Hamilton. The Ricci soliton is defined by a vector field and it is a natural generalization of the Einstein metric. We have shown earlier that the vector field of the Ricci soliton is an infinitesimal harmonic transformation. In our paper, we survey Ricci solitons geometry as an application of the theory of infinitesimal harmonic transformations.
On holomorphically projective mappings onto Kählerian spaces
The main result of this paper determines a system of linear partial differential equations of Cauchy type whose solutions correspond exactly to holomorphically projective mappings of a given equiaffine space onto a Kählerian space. The special case of constant holomorphic curvature is also studied.
-semisymmetric spaces and concircular vector fields
On almost geodesic mappings of the type of Riemannian spaces preserving a system -orthogonal hypersurfaces
On Uniqueness Theoremsfor Ricci Tensor
In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold and a symmetric 2-tensor , construct a metric on whose Ricci tensor equals . In particular, DeTurck and Koiso proved the following celebrated result: the Ricci curvature uniquely determines the Levi-Civita connection on any compact Einstein manifold with non-negative section curvature. In the present paper we generalize the result of DeTurck and Koiso for a Riemannian manifold with non-negative...
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