On conformally symmetric 2-Ricci-recurrent spaces
On conformally symmetric Ricci-recurrent spaces
On Curvature Characterizations of Some Hypersurfaces in Spaces of Constant Curvature
On curvature collineations on simple conformally recurrent manifolds
On Decomposable Almost Pseudo Conharmonically Symmetric Manifolds
The object of the present paper is to study decomposable almost pseudo conharmonically symmetric manifolds.
On density concomitants of the covariant curvature tensor in the two- and three-dimensional Riemann space
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...
On four-dimensional Riemannian warped product manifolds satisfying certain pseudo-symmetry curvature conditions
On Gauss-Bonnet Theorem
On geodesic and holomorphically projective mappings of generalized recurrent spaces.
On geodesic lines of metric semi-symmetric connection on Riemannian and hyperbolic Kaehlerian spaces.
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 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 holomorphically projective mappings of -Kähler manifolds
In this paper we study fundamental equations of holomorphically projective mappings of -Kähler spaces (i.e. classical, pseudo- and hyperbolic Kähler spaces) with respect to the smoothness class of metrics. We show that holomorphically projective mappings preserve the smoothness class of metrics.
On Hypercylinders in Conformally Symmetric Manifolds
On hypersurfaces in space forms satisfying particular curvature conditions of Tachibana type
On manifolds satisfying some curvature conditions
On metrizability of locally homogeneous affine 2-dimensional manifolds
In [19] we proved a theorem which shows how to find, under particular assumptions guaranteeing metrizability (among others, recurrency of the curvature is necessary), all (at least local) pseudo-Riemannian metrics compatible with a given torsion-less linear connection without flat points on a two-dimensional affine manifold. The result has the form of an implication only; if there are flat points, or if curvature is not recurrent, we have no good answer in general, which can be also demonstrated...
On Metrizable Locally Homogeneous Connections in Dimension
We discuss metrizability of locally homogeneous affine connections on affine 2-manifolds and give some partial answers, using the results from [Arias-Marco, T., Kowalski, O.: Classification of locally homogeneous affine connections with arbitrary torsion on 2-dimensional manifolds. Monatsh. Math. 153 (2008), 1–18.], [Kowalski, O., Opozda, B., Vlášek, Z.: A classification of locally homogeneous connections on 2-dimensional manifolds vis group-theoretical approach. CEJM 2, 1 (2004), 87–102.], [Vanžurová,...
On natural metrics on tangent bundles of Riemannian manifolds
There is a class of metrics on the tangent bundle of a Riemannian manifold (oriented , or non-oriented, respectively), which are ’naturally constructed’ from the base metric [Kow-Sek1]. We call them “-natural metrics" on . To our knowledge, the geometric properties of these general metrics have not been studied yet. In this paper, generalizing a process of Musso-Tricerri (cf. [Mus-Tri]) of finding Riemannian metrics on from some quadratic forms on to find metrics (not necessary Riemannian)...