The Cauchy problem for Lorentz metrics with prescribed Ricci curvature
The characterization of the spherical timelike curves in 3-dimensional Lorentzian space.
The Clairaut's theorem on rotational surfaces in pseudo-Euclidean 4-space with index 2
Clairaut’s theorem is expressed on the surfaces of rotation in semi Euclidean 4-space. Moreover, the general equations of time-like geodesic curves are characterized according to the results of Clairaut's theorem on the hyperbolic surfaces of rotation and the elliptic surface of rotation, respectively.
The Euler theorem and Dupin indicatrix for surfaces at a constant distance from edge of regression on a surface in
The first eigenvalue of spacelike submanifolds in indefinite space form
In this paper, we prove that the first eigenvalue of a complete spacelike submanifold in with the bounded Gauss map must be zero.
The First Order PDE System for Type III Osserman Manifolds
The Gauss map of a spacelike constant mean curvature hypersurface of Minkowski space.
The Gauss-Bonnet theorem for Cayley-Klein geometries of dimension two.
The geometrical interpretation of temporal cone norm in almost Minkowski manifold.
The Group of Invertible Elements of the Algebra of Quaternions
We have, that all two-dimensional subspaces of the algebra of quaternions, containing a unit, are 2-dimensional subalgebras isomorphic to the algebra of complex numbers. It was proved in the papers of N. E. Belova. In the present article we consider a 2-dimensional subalgebra of complex numbers with basis and we construct the principal locally trivial bundle which is isomorphic to the Hopf fibration.
The isotropic 3-sphere.
The local structure of essentially conformally symmetric manifolds with constant fundamental function II. The hyperbolic case
The local structure of essentially conformally symmetric manifolds with constant fundamental function I. The elliptic case
The local structure of essentially conformally symmetric manifolds with constant fundamental function. III. The parabolic case
The metrics of a twodimensional space with geodesics represented by a linear equation
The nonexistence of rank 4 IP tensors in signature .
The Plane-Time in Which Paths of Inertional Motions Are Conics
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.
The structure of reachable sets for affine control systems induced by generalized Martinet sub-lorentzian metrics
In this paper we investigate analytic affine control systems q̇ = X + uY, u ∈ [a,b] , where X,Y is an orthonormal frame for a generalized Martinet sub-Lorentzian structure of order k of Hamiltonian type. We construct normal forms for such systems and, among other things, we study the connection between the presence of the singular trajectory starting at q0 on the boundary of the reachable set from q0 with the minimal number of analytic functions needed for describing the reachable set from q0.
Theorems concerning certain special tensor fields on Riemannian manifolds and their applications.