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The aim of the present paper is to investigate intrinsically the notion of a concircular π-vector field in Finsler geometry. This generalizes the concept of a concircular vector field in Riemannian geometry and the concept of concurrent vector field in Finsler geometry. Some properties of concircular π-vector fields are obtained. Different types of recurrence are discussed. The effect of the existence of a concircular π-vector field on some important special Finsler spaces is investigated. Almost all results obtained in this work are formulated in a coordinate-free form.
The main aim of the present paper is to establish an intrinsic
investigation of the energy β-conformal
change of the most important special Finsler spaces, namely, Ch-recurrent,
Cv-recurrent, C0-recurrent, Sv-recurrent,
quasi-C-reducible, semi-C-reducible, C-reducible, P-reducible, C2-like,
S3-like, P2-like and h-isotropic, ···, etc. Necessary
and sufficient conditions for such special Finsler manifolds to be invariant
under an energy β-conformal change
are obtained. It should be pointed out that the present work is formulated in a
prospective modern coordinate-free form.