A ug 2 00 9 Generalized β - conformal change of Finsler metrics ∗
نویسندگان
چکیده
In this paper, we introduce and investigate a general transformation or change of Finsler metrics, which is referred to as a generalized β-conformal change: L(x, y) −→ L(x, y) = f(eL(x, y), β(x, y)). This transformation combines both β-change and conformal change in a general setting. The change, under this transformation, of the fundamental Finsler connections, together with their associated geometric objects, are obtained. Some invariants and various special Finsler spaces are investigated under this change. The most important changes of Finsler metrics existing in the literature are deduced from the generalized β-conformal change as special cases.
منابع مشابه
Ju n 20 09 Generalized β - conformal change of Finsler metrics
In this paper, we introduce and investigate a general transformation or change of Finsler metrics, which is referred to as a generalized β-conformal change: L(x, y) −→ L(x, y) = f(eL(x, y), β(x, y)). This transformation combines both β-change and conformal change in a general setting. The change, under this transformation, of the fundamental Finsler connections, together with their associated g...
متن کاملOn conformal transformation of special curvature of Kropina metrics
An important class of Finsler metric is named Kropina metrics which is defined by Riemannian metric α and 1-form β which have many applications in physic, magnetic field and dynamic systems. In this paper, conformal transformations of χ-curvature and H-curvature of Kropina metrics are studied and the conditions that preserve this quantities are investigated. Also it is shown that in the ...
متن کاملGeneralized Douglas-Weyl Finsler Metrics
In this paper, we study generalized Douglas-Weyl Finsler metrics. We find some conditions under which the class of generalized Douglas-Weyl (&alpha, &beta)-metric with vanishing S-curvature reduce to the class of Berwald metrics.
متن کاملar X iv : 0 80 5 . 25 99 v 3 [ m at h . D G ] 2 6 A ug 2 00 9 CONCURRENT π - VECTOR FIELDS AND ENERGY β - CHANGE
The present paper deals with an intrinsic investigation of the notion of a concurrent π-vector field on the pullback bundle of a Finsler manifold (M,L). The effect of the existence of a concurrent π-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular β-change, namely the energy β-change (L̃(x, y) = L(x, y) + B(x, y)with B := g(ζ, η); ζ bei...
متن کاملCartan Connections Associated to a Β-conformal Change in Finsler Geometry
On a Finsler manifold (M,L), we consider the change L −→ L(x, y) = eL(x, y) + β(x, y), which we call a β-conformal change. This change generalizes various types of changes in Finsler geometry: conformal, C-conformal, h-conformal, Randers and generalized Randers changes. Under this change, we obtain an explicit expression relating the Cartan connection associated to (M,L) and the transformed Car...
متن کامل