  Let $X$ be a smooth complex projective variety. A recent conjecture of S.
Kov\'acs states that if t\ he $p^{\text{th}}$-exterior power of the tangent
bundle $T_X$ contains the $p^{\text{th}}$-exterior power of an ample vector
bundle, then $X$ is either a projective space or a smooth quadric hypersurface.
This conjecture is appealing since it is a common generalization of Mori's,
Wahl's, Andreatt\ a-W\'isniewski's, and Araujo-Druel-Kov\'acs's
characterizations of these spaces. In this paper I give a proof affirming this
conjecture for varieties with Picard number 1.
