Fe b 20 06 Conformal β - change in Finsler spaces

We investigate what we call a conformal β-change in Finsler spaces, namely L(x, y) → * L(x, y) = e σ(x) L(x, y) + β(x, y) where σ is a function of x only and β(x, y) is a given 1-form. This change generalizes various types of changes: conformal changes, Randers changes and β-changes. Under this change, we obtain the relationships between some tensors associated with (M, L) and the corresponding tensors associated with (M, * L). We investigate some σ-invariant tensors. This investigation allows us to give an answer to the question: Are the properties of C-reducibility, S 3-likeness and S 4-likeness invariant under a conformal β-change?