The power of the tangent bundle of the real projective space, its complexification and extendibility

Abstract

We establish the formulas on the power τ k \tau ^k of the tangent bundle τ = τ ( R P n ) \tau =\tau (RP^n) of the real projective n n -space R P n RP^n and its complexification c τ k c\tau ^k , and apply the formulas to the problem of extendibility and stable extendiblity of τ k \tau ^k and c τ k c\tau ^k .