Stably extendible tangent bundles over lens spaces

The purpose of this paper is to study the stable extendibility of the tangent bundle τ n ( p ) over the ( 2 n + 1 ) -dimensional standard lens space L n ( p ) for odd prime p. We investigate for which m the tangent bundle τ n ( p ) is stably extendible to L m ( p ) but is not stably extendible to L m + 1 ( p ) , where we consider m = ∞ if τ n ( p ) is stably extendible to L k ( p ) for any k ⩾ n , and determine m in the case n ⩾ p − 3 .