n] be an n-dimensional

differentiable manifold endowed with a (1,1) tensor field [phi], a contravariant vector field [xi], a covariant vector field [eta] and a Lorentzian metric g of type (0, 2) such that for each point p [member of] M, the tensor [g.

1)-dimensional

differentiable manifold endowed with an almost contact metric structure ([phi], [xi], [eta] g).

Let (M, L) be a Finsler space, where M is an n-dimensional

differentiable manifold associated with the fundamental function L.

Let M be a real 2m-dimensional

differentiable manifold.

As we have suggested, a rate distortion manifold need not necessarily be a

differentiable manifold in the conventional sense, but may admit an abstract differentiable space structure (such as that described in Appendix III).

An alternative to the usual approach via the Frobenius integrability conditions was proposed in an article of 1972 in which I defined a differentiable preference relation by the requirement that the indifferent pairs of commodity vectors from a

differentiable manifold.

A non flat n-dimensional

differentiable manifold [M.

A semi-symmetric linear connection in a

differentiable manifold was introduced by Friedmann and Schouten in [5].

Roughly speaking, a

differentiable manifold (hereafter manifold) is a topological space whose local equivalence to Euclidean space permits a global calculus.

In 1924, Friedman and Schouten introduced the notion of semi-symmetric linear connection on a

differentiable manifold.

Recall that a Riemannian manifold is a

differentiable manifold that is equipped with a metric.

If on an odd dimensional

differentiable manifold [M.