arXiv subjects
Publications and source records attributed to Valerii Dryuma.
On base of three-dimensional flat metrics obtained with the help of solutions of the KdV-equation were constructed the examples of six-dimensional metrics, which are determined by the help of solutions of Krichever-Novikov and KdV. Their properties are discussed.
The examples of solutions of the system of differential equations generated by the Hopf map $S^3\rightarrow S^2$ are constructed. Their properties are discussed.
An examples of the Ricci-flat metric associated with the equations of Navier-Stokes are constructed. Their properties are investigated.
The examples of the Ricci flows on four-dimendionsl manifolds which are determined by help of nonlinear differentials equations of the type of Monge-Ampere are constructed. Their particular solutions and their properties are discussed.
An examples of solutions of the equation for curvature of congruence of cycles are constructed. Their properties are discussed.
The method of point transformation of the functions and variables for construction of particular solutions of the Equations of Nonstationary Transonic Gas Flows is used.
The relations between the second order ODE's cubical on the first derivative and their dual equations are discussed
Some solutions of the Heavenly equations and their generalizations are considered
An examples of a Ricci-flat of four-dimensional spaces with a Walker metrics and their generalizations are constructed. The properties of corresponding geodesic equations are discussed.
The examples of ten-dimensional vacuum Einstein spaces composed of four-dimensional Einstein spaces and six-dimensional Ricci-flat base space defined by the solutions of the Korteveg de-Vries equation are constructed.
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 of geodesics and asymptotic lines are used.