For a Nakano semipositive vector bundle
(E, h) on X, we have an isomorphism
We therefore propose to represent them as a vector bundle
< with an added information loop: O.
We can consider PTM as the base manifold of the vector bundle
P*TM, pulled back with the canonical projection map p: PTM [right arrow] M defined by p([x.
The vector bundle
that is constituted by choosing a screen space each point of M is said to be a screen distribution on M, denoted by S(TM).
Let E [right arrow] X be a smooth vector bundle
over an n-manifold X.
2], g) a Riemannian surface endowed with a rank 2 vector bundle
E endowed with a metric and a compatible connection [[nabla].
k]M has a multiple vector bundle
structure with k projections onto [T.
0](X), with multiplication given by [E][F] = [E [cross product] F] where E is a vector bundle
and F a coherent sheaf.
1](R,M) is regarded as a vector bundle
over the product manifold R x M, having the fibre type [R.
In  Lazarsfeld and the author proved that the polynomials in the Chern classes of a vector bundle
that are positive whenever the bundle is ample are exactly those polynomials that are positive linear combinations of the Schur polynomials.
By definition, the Euler class of the vector bundle
associated to the reduced regular representation [[?
Given a smooth complex vector bundle
[xi], represented by an idempotent matrix [phi] of order n, over the ring of smooth functions on the base, the Chern classes of [xi] in the standard de Rham cohomology of differential forms, are given as follows: