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

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.

laTeX file, 18 pages, some typos corrected, some proofs added, concluding summary added at the end of the paper. arXiv admin note: text overlap with arXiv:0805.2599