Abstract
The purpose of this paper is to study extendibility and stable extendibility of vector bundles over real projective spaces. We determine a necessary and sufficient condition that a vector bundle ζ over the real projective n-space RPn is extendible (or stably extendible) to RPm for every m>n in the case where ζ is the complexification of the tangent bundle of RPn and in the case where ζ is the normal bundle associated to an immersion of RPn in the Euclidean (n+k)-space Rn+k or its complexification, and give examples of the normal bundle which is extendible to RPN but is not stably extendible to RPN+1.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have