Related papers: Riemann extensions in theory of the first order sy…
Theory of Riemann Extensions of the spaces with constant affine connection for the studying of the properties of nonlinear the first order systems of differential equations is proposed. Quadratic planar system of equations and the Lorenz…
Geometrical properties of holonomic and non holonomic varieties defined by the Pfaff equations connected with a first order systems of differential equations are studied. The Riemann extensions of affine connected spaces for investigation…
Some examples of three-dimensional metrics of constant curvature defined by solutions of nonlinear integrable differential equations and their generalizations are constructed. The properties of Riemann extensions of the metrics of constant…
Some properties of the 4-dim Riemannian spaces with the metrics $$ ds^2=2(za_3-ta_4)dx^2+4(za_2-ta_3)dxdy+2(za_1-ta_2)dy^2+2dxdz+2dydt $$ associated with the second order nonlinear differential equations $$…
A generalization of the already studied transformations of the linear differential equation into a system of the first order equations is given. The proposed transformation gives possibility to get new forms of the N-dimensional system of…
The theory of superposition rules for solutions of a Lie system of first-order differential equations is extended to deal with analogous systems of second-order and the theory is illustrated with the very rich example of Ermakov-like…
Riemann extension for the anti Mach metric is derived, the solution of geodesic equations for the extended space are given, some properties for the extended space was studied and compared with the basic space and the constructions of a…
Some properties of the G\"odel space-time metric and its Riemann extension are studied
Use of certain non-commuting variables is considered in first-order differential equations. Superspace variables are discussed within the setting of first-order ordinary differential equations and n-ary algebras. Results on quadratic…
A natural extension of Riemannian geometry to a much wider context is presented on the basis of the iterated differential form formalism developed in math.DG/0605113 and an application to general relativity is given.
On a basis of theory of Riemann extension of the space of constant affine connection associated with the R\"ossler system of equations relations between its parameters are investigated.
In this thesis, we study extensions of the theory of Riemannian submanifolds in two directions. First, we will show how Riemannian geometry and submanifold theory in particular, can be generalized using the notion of 'Rinehart spaces', and…
We extend to Riemannian manifolds the theory of conditioned stochastic differential equations. We also provide some enlargement formulas for the Brownian filtration in this nonflat setting.
Formulations of some Grassmann-valued systems of ordinary differential equations invariant under (infinitesimal) supersymmetry transformations, including $N$-superspace extended types, are reviewed and discussed, with use of superfields.…
Basic aspects of differential geometry can be extended to various non-classical settings: Lipschitz manifolds, rectifiable sets, sub-Riemannian manifolds, Banach manifolds, Weiner space, etc. Although the constructions differ, in each of…
An examples of multidimensional the Ricci-flat spaces defined by nonlinear differential equations are constructed. Their properties are discussed.
Some properties of eight-dimensional Riemann extension of Minkowsky space-time metric in rotating coordinate system are studied.
We study first-order expansions of the reals which do not define the set of natural numbers. We also show that several stronger notions of tameness are equivalent to each others.
We lay foundations of the subject in the title, on which we build in another paper devoted to isometries in spaces of K\"ahler metrics.
We prove a number of results on the geometry associated to the solutions of evolution equations given by first-order differential operators on manifolds. In particular, we consider distance functions associated to a first-order operator,…