Stable extendibility of vector bundles over lens spaces mod 3 and the stable splitting problem

Let Ln(3) denote the (2n+1)-dimensional standard lens space mod 3. In this paper, we study the conditions for a given real vector bundle over Ln(3) to be stably extendible to Lm(3) for every m⩾n, and establish the formula on the power ζk=ζ⊗⋯⊗ζ (k-fold) of a real vector bundle ζ over Ln(3). Moreover, we answer the stable splitting problem for real vector bundles over Ln(3) by means of arithmetic conditions.