The Fundamental Equations of Minimal Surfaces in C2.
The gap phenomenon in the dimension study of finite type systems
Several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the symmetries of geometric structures and differential equations. A general result clarifying this effect in the case when the structure is associated to a vector distribution, is proposed.
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 geometric structure of the inverse gamma distribution.
The geometric structure of the Pareto distribution.
The geometrical interpretation of temporal cone norm in almost Minkowski manifold.
The geometry of the space of Cauchy data of nonlinear PDEs
First-order jet bundles can be put at the foundations of the modern geometric approach to nonlinear PDEs, since higher-order jet bundles can be seen as constrained iterated jet bundles. The definition of first-order jet bundles can be given in many equivalent ways - for instance, by means of Grassmann bundles. In this paper we generalize it by means of flag bundles, and develop the corresponding theory for higher-oder and infinite-order jet bundles. We show that this is a natural geometric framework...
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 homological Kähler-de Rham differential mechanism. I: Application in general theory of relativity.
The Induced Connections on the Subspaces in Miron's Osckm
The induced TMA-connections of a Finslerian hypersurface
The information geometric descriptions of denormalized thermodynamic manifolds.
The initial value problem of the Poincaré gauge theory in vacuum. II. First order formalism
The initial value problem of the Poincaré gauge theory in vacuum. I. Second order formalism
The inverse problem of the calculus of variations for Finsler structures
The isotropic 3-sphere.
The Jordan normal form of higher order Osserman algebraic curvature tensors
We construct new examples of algebraic curvature tensors so that the Jordan normal form of the higher order Jacobi operator is constant on the Grassmannian of subspaces of type in a vector space of signature . We then use these examples to establish some results concerning higher order Osserman and higher order Jordan Osserman algebraic curvature tensors.
The kaehlerian structures and reproducing kernels
It is shown that one can define a Hilbert space structure over a kaehlerian manifold with global potential in a natural way.
The -dual of an Finsler space of order two.