vector bundle

(redirected from Real vector bundle)

vector bundle

[′vek·tər ‚bən·dəl]
(mathematics)
A locally trivial bundle whose fibers are isomorphic vector spaces.
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Let F [right arrow] X be a smooth real vector bundle of rank n with orthogonal connection [D.
Let V [right arrow] Y be a real vector bundle of rank n over a manifold Y given by transition functions [g.
Consider a smooth real vector bundle E [right arrow] X of rank m, and let [pi] : [G.
2 for morphisms [alpha] : E [right arrow] F of real vector bundles.
Throughout this section X will be an oriented manifold and E [right arrow] X and F [right arrow] X will be smooth, real vector bundles furnished with orthogonal connections [D.
Let U [right arrow] Y and F [right arrow] Y be real vector bundles with rank (U) = m and rank (F) = n, and set H = Hom (U,F) = [U.