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Let X be a smooth projective surface over C and let L be a line bundle on Xgenerated by its global sections. Let f:X-->P^r be the morphism associated to Land let T be the tangent bundle of P^r; we investigate the \mu-stability of f*Twith respect to L when X is either a regular surface with p_g=0, a K3 surfaceor an abelian surface. In particular, we show that it is \mu-stable when X isK3 and L is ample and when X is abelian and L^2>13.

About the stability of the tangent bundle of P^n restricted to a surface