  We establish a new universal relation between the Lie bracket and
$\circ$-multiplication of tangent fields on any Frobenius (super)manifold. We
use this identity in order to introduce the notion of ``weak Frobenius
manifold'' which does not involve metric as part of structure. As another
application, we show that the powers of an Euler field generate (a half of) the
Virasoro algebra on an arbitrary, not necessarily semisimple, Frobenius
supermanifold.
