On projective two-dimensional Finsler spaces with special metric

TL;DR

This paper introduces Kropina spaces, a special class of two-dimensional Finsler spaces, providing foundational insights into their structure and properties, originally published in 1958 and translated into English.

Contribution

It presents the initial introduction and analysis of Kropina spaces, a unique class within Finsler geometry, expanding the understanding of special metric spaces.

Findings

Defined the structure of Kropina spaces

Analyzed properties specific to two-dimensional Finsler spaces

Laid groundwork for future research in Finsler geometry

Abstract

We present the English translation of the paper where one special class of Finsler spaces was introduced. Now this class is known as so called "Kropina spaces". The article was written in 1958 and published in Russian in "Trudy seminara po vektornomu i tenzornomu analizu" ("Workshops of the Seminar in vector and tensor Analysis"), vol. XI, 1961.