On geometrical properties of the spaces defined by the Pfaff equations

TL;DR

This paper investigates the geometric properties of spaces defined by Pfaff equations, focusing on holonomic and non-holonomic varieties, using Riemann extensions to analyze geodesics and asymptotic lines.

Contribution

It provides a detailed geometric analysis of spaces defined by Pfaff equations, incorporating Riemann extensions to explore their geodesic and asymptotic structures.

Findings

Characterization of holonomic and non-holonomic varieties

Application of Riemann extensions to study geodesics

Insights into asymptotic lines in these spaces

Abstract

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.