Harmonic 4-Spaces.
Higher order Codazzi tensors on conformally flat spaces.
Holomorphically projective mappings of compact semisymmetric manifolds
In this paper we consider holomorphically projective mappings from the compact semisymmetric spaces onto (pseudo-) Kählerian spaces . We proved that in this case space is holomorphically projective flat and is space with constant holomorphic curvature. These results are the generalization of results by T. Sakaguchi, J. Mikeš, V. V. Domashev, N. S. Sinyukov, E. N. Sinyukova, M. Škodová, which were done for holomorphically projective mappings of symmetric, recurrent and semisymmetric Kählerian...
Infinitesimal aspects of the Laplace operator.
Infinitesimal bending of a subspace of a space with non-symmetric basic tensor
In this work infinitesimal bending of a subspace of a generalized Riemannian space (with non-symmetric basic tensor) are studied. Based on non-symmetry of the connection, it is possible to define four kinds of covariant derivative of a tensor. We have obtained derivation formulas of the infinitesimal bending field and integrability conditions of these formulas (equations).
Information geometry of the power inverse Gaussian distribution.
Interaction of Tubes and Spheres.
Invariant metrics on the tangent bundle of a homogeneous space
Invariant operators on real and complex manifolds.
Jacobi maps between Riemannian manifolds.
Jet isomorphism for conformal geometry
Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite order ambient lift for conformal densities in the case in which harmonic extension is obstructed is described. A jet isomorphism theorem for even dimensional conformal geometry is formulated using the inhomogeneous ambient metrics recently introduced by the author...
Kähler manifolds of quasi-constant holomorphic sectional curvatures
The Kähler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kähler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the geometric angle, associated with the section. A curvature identity characterizing such manifolds is found. The biconformal group of transformations whose elements transform Kähler metrics into Kähler ones is introduced and biconformal tensor invariants are obtained....
Krümmungstreue Diffeomorphismen Riemannscher und pseudo-Riemannscher Mannigfaltigkeiten.
Local isometry classes of Riemannian -manifolds with constant Ricci eigenvalues
Lokale Geometrie des Radius in Riemannschen Mannigfaltigkeiten II
Lokale Geometrie des Radius in Riemannschen Mannigfaltigkeiten I
Mean and scalar curvature homogeneous Riemannian manifolds.
Metric of special 2F-flat Riemannian spaces
In this paper we find the metric in an explicit shape of special -flat Riemannian spaces , i.e. spaces, which are -planar mapped on flat spaces. In this case it is supposed, that is the cubic structure: .
Metrizability of connections on two-manifolds
We contribute to the reverse of the Fundamental Theorem of Riemannian geometry: if a symmetric linear connection on a manifold is given, find non-degenerate metrics compatible with the connection (locally or globally) if there are any. The problem is not easy in general. For nowhere flat -manifolds, we formulate necessary and sufficient metrizability conditions. In the favourable case, we describe all compatible metrics in terms of the Ricci tensor. We propose an application in the calculus of...
Metrization of connections with regular curvature
We discuss Riemannian metrics compatible with a linear connection that has regular curvature. Combining (mostly algebraic) methods and results of [4] and [5] we give an algorithm which allows to decide effectively existence of positive definite metrics compatible with a real analytic connection with regular curvature tensor on an analytic connected and simply connected manifold, and to construct the family of compatible metrics (determined up to a scalar multiple) in the affirmative case. We also...