Tangent bundle geometry induced by second order partial differential equations

Recurrent metrics in the geometry of second order differential equations

Given a pair (semispray $S$, metric $g$) on a tangent bundle, the family of nonlinear connections $N$ such that $g$ is recurrent with respect to $(S, N)$ with a fixed recurrent factor is determined by using the Obata tensors. In particular, we obtain a characterization for a pair $(N, g)$ to be recurrent as well as for the triple $(S, stackrel{c}{N}, g)$ where $stackrel{c}{N}$ is the canonical ...

recurrent metrics in the geometry of second order differential equations

given a pair (semispray $s$, metric $g$) on a tangent bundle, the family of nonlinear connections $n$ such that $g$ is recurrent with respect to $(s, n)$ with a fixed recurrent factor is determined by using the obata tensors. in particular, we obtain a characterization for a pair $(n, g)$ to be recurrent as well as for the triple $(s, stackrel{c}{n}, g)$ where $stackrel{c}{n}$ is the canonical ...

THE CARTAN-WEYL CONFORMAL GEOMETRY OF A PAIR OF SECOND-ORDER PARTIAL-DIFFERENTIAL EQUATIONS by

We explore the conformal geometric structures of a pair of second-order partial-differential equations. In particular, we investigate the conditions under which this geometry is conformal to the vacuum Einstein equations of general relativity. Furthermore, we introduce a new version of the conformal Einstein equations, which are used in the analysis of the conformal geometry of the PDE’s.

Solving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation

In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...

The Solution of Second - Order Partial Differential Equations