A sufficient condition is derived for a finite-time $L_2 $ singularity of the 3d incompressible Euler equations, making appropriate assumptions on eigenvalues of the Hessian of pressure. Under this condition $ \ \lim_{ t \uparrow T_*} \sup \|\frac{ D \omega} { Dt}\|_{L_2(\Omega)} = \infty $, where $\Omega \subset \mathbb{R}$ moves with the fluid. In particular, $| \omega | $, $| \S_{ij} | $, and $| \P_{ij} | $ all become unbounded at one point $(x_1, T_1) $, $T_1 $ being the first blow-up time in $L_2 $.