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

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