A geometric procedure is elaborated for transforming (pseudo) Riemanian metrics and connections into canonical geometric objects (metric and nonlinear and linear connections) for effective Lagrange, or Finsler, geometries which, in their turn, can be equivalently represented as almost Kähler spaces. This allows us to formulate an approach to quantum gravity following standard methods of deforma...

Let E : 0 → S → E → Q → 0 be a short exact sequence of hermitian vector bundles with metrics on S and Q induced from that on E. We compute the Bott-Chern form φ̃(E ) corresponding to any characteristic class φ, assuming E is projectively flat. The result is used to obtain a new presentation of the Arakelov Chow ring of the arithmetic Grassmannian.

We use two non-Riemannian curvature tensors, the χ-curvature and mean Berwald to characterise a class of Finsler metrics admitting first integrals. This includes constant flag curvature.

In this paper, we study the class of cubic (\alpha, \beta)-metrics. We show that every weakly Landsberg \beta)-metric has vanishing S-curvature. Using it, prove is a metric if and only it Berwald metric. This yields an extension Matsumoto's result for