On generalized recurrent Kaehlerian manifolds of second order I
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 of recurrent Finsler 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 geometry of curves of flags of constant type
We develop an algebraic version of Cartan’s method of equivalence or an analog of Tanaka prolongation for the (extrinsic) geometry of curves of flags of a vector space W with respect to the action of a subgroup G of GL(W). Under some natural assumptions on the subgroup G and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure linear algebra. The scope...
On Growth and Form and Geometry. I
On Hamiltonian submanifolds.
On Hb-flat Hyperbolic Kaehlerian Spaces
On higher order geometry on anchored vector bundles
Some geometric objects of higher order concerning extensions, semi-sprays, connections and Lagrange metrics are constructed using an anchored vector bundle.
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.
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 homogeneous conformally symmetric pseudo-Riemannian manifolds
On Hypercylinders in Conformally Symmetric Manifolds
On hypersurfaces in space forms satisfying particular curvature conditions of Tachibana type
On invariant operations on pseudo-Riemannian manifolds
Invariant polynomial operators on Riemannian manifolds are well understood and the knowledge of full lists of them becomes an effective tool in Riemannian geometry, [Atiyah, Bott, Patodi, 73] is a very good example. The present short paper is in fact a continuation of [Slovák, 92] where the classification problem is reconsidered under very mild assumptions and still complete classification results are derived even in some non-linear situations. Therefore, we neither repeat the detailed exposition...
On invariant submanifolds in almost cosymplectic manifolds
On isometric immersions into complex space forms.
On isotropic Berwald metrics
We prove that every isotropic Berwald metric of scalar flag curvature is a Randers metric. We study the relation between an isotropic Berwald metric and a Randers metric which are pointwise projectively related. We show that on constant isotropic Berwald manifolds the notions of R-quadratic and stretch metrics are equivalent. Then we prove that every complete generalized Landsberg manifold with isotropic Berwald curvature reduces to a Berwald manifold. Finally, we study C-conformal changes of isotropic...