Concircular $\pi$-Vector Fields and Special Finsler Spaces

TL;DR

This paper explores the concept of concircular π-vector fields in Finsler geometry, generalizing classical notions and examining their properties and effects on special Finsler spaces in a coordinate-free framework.

Contribution

It introduces and studies the properties of concircular π-vector fields in Finsler geometry, extending known concepts from Riemannian and Finsler contexts.

Findings

Properties of concircular π-vector fields are established.

The influence of these fields on special Finsler spaces is analyzed.

Different recurrence types related to these fields are discussed.

Abstract

The aim of the present paper is to investigate intrinsically the notion of a concircular $\pi$-vector field in Finsler geometry. This generalizes the concept of a concircular vector field in Riemannian geometry and the concept of a concurrent vector field in Finsler geometry. Some properties of concircular $\pi$-vector fields are obtained. Different types of recurrence are discussed. The effect of the existence of a concircular $\pi$-vector field on some important special Finsler spaces is investigated. The whole work is formulated in a coordinate-free form.