A Riemannian almost product structure on a manifold induces on a submanifold of codimension 1 a structure generalizing the paracontact structures and containing a Riemannain metric and an one form . We show that the pair consisting of this Riemannian metric and one form defines a strongly convex Randers metric on submanifold. We establish some properties of this Randers metric and we provide so...

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...

A Finsler metric is of sectional flag curvature if its flag curvature depends only on the section. In this article, we characterize Randers metrics of sectional flag curvature. It is proved that any non-Riemannian Randers metric of sectional flag curvature must have constant flag curvature if the dimension is greater than two. 0. Introduction Finsler geometry has a long history dated from B. Ri...

in this paper, we study a class of finsler metrics which contains the class of p-reducible andgeneral relatively isotropic landsberg metrics, as special cases. we prove that on a compact finsler manifold,this class of metrics is nothing other than randers metrics. finally, we study this class of finsler metrics withscalar flag curvature and find a condition under which these metrics reduce to r...

Using the relativistic Fermat’s principle, we establish a bridge between stationary–complete manifolds which satisfy observer-manifold condition and pre-Randers metrics, namely, Randers metrics without any restriction on one-form. As consequence, give description of causal ladder such spacetimes in terms elements associated with metric: its geodesics distance. We obtain, as applications this in...

We give a necessary and sufficient condition on a Randers space for the existence of a measure for which Shen’s S-curvature vanishes everywhere. Moreover, such a measure coincides with the Busemann-Hausdorff measure up to a constant multiplication.