A vector bundle is a fibre bundle with the fibre a vector space, or . The structure group will be .

Example: let dim(M)=m manifold be embedded in . Then TM is a vector bundle. . There exists orthogonal vector space, . This can be unioned over p to get

source psfile jl@crush.caltech.edu index holomorphic_vector_bundle associated_vector_bundle holomorphic_line_bundle splitting_principle whitney_sum_bundle Chern-Weil_theorem tensor_product null_section line_bundle chern_class