Let $V\subset\mathbb{P}^n$ be a projective variety and $C_V$ its conormal subvariety in $T^\ast\mathbb{P}^n$. Denote by $\mathscr{O}_{C_V}$ its structure sheaf, then when will the condition
$\mathit{Ext}^1(\mathscr{O}_{C_V},\mathscr{O}_{C_V})=0$
hold for $V$?