The Geometry of Myller Configurations. Applications to Theory of Surfaces and Nonholonomic Manifolds

TL;DR

This paper explores the geometric properties of Myller configurations, introducing invariants and generalizations of classical concepts, with applications to surfaces and nonholonomic manifolds.

Contribution

It provides a comprehensive framework for Myller configurations, including invariants, parallelism, and applications to advanced geometric structures.

Findings

Introduction of invariants for Myller configurations

Generalization of Levi-Civita parallelism

Applications to surfaces and nonholonomic manifolds

Abstract

The book contents: the notion of Myller configurations, Darboux frame, fundamental formulae and fundamental theorem of existence. The complete system of invariants allows to introduce the notions of Myller parallelism and concurrence as well as a famous Klein's formula. By way it is obtained an important generalization of the Levi-Civita parallelism. The applications to the theory of surfaces and nonholonomic manifolds end the book.