Parallelism and Equidistance in Classical Differential Geometry

Classical Differential Geometry

Convex Solutions of Elliptic Differential Equations in Classical Differential Geometry

The issue of convexity is fundamental in the theory of partial differential equations. We discuss some recent progress of convexity estimates for solutions of nonlinear elliptic equations arising from some classical problems in differential geometry. We first review some works in the literature on the convexity of solutions of quasilinear elliptic equations in Rn. The study of geometric propert...

Parallelism in diagram geometry

We introduce the concept of parallelism in diagram geometry, we apply it to a new gluing concept that provides geometries of higher rank, we combine it with another recent extension procedure for geometries and collect many examples solving existence questions for geometries over specified diagrams.

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 ...

On Curvature Tensors in Absolute Parallelism Geometry

In this paper we discuss curvature tensors in the context of Absolute Parallelism geometry. Different curvature tensors are expressed in a compact form in terms of the torsion tensor of the canonical connection. Using the Bianchi identities some other identities are derived from the expressions obtained. These identities, in turn, are used to reveal some of the properties satisfied by an intrig...