Concircular $π$-Vector Fields and Special Finsler Spaces

Nabil L. Youssef, A. Soleiman

Published 2012-08-14, updated 2013-01-14Version 3

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.