For shallow geometry of surface in Monge form using rectangular $z=f(x,y)$ we have from classical St. Venant relation

$$  \dfrac{\partial ^2{\epsilon_x}}{{\partial {y^2}} }++  \dfrac{\partial ^2{\epsilon_y}}{{\partial {x^2}} }++ \dfrac{\partial ^2{\epsilon_{xy}}} {\partial {x}\partial {y} }++  $$

that is known to represent Gauss curvature as derived by . It links direct and shear strains for compatibilty.

$$  \dfrac{\partial ^2{\epsilon_x}}{{\partial {y^2}} }++  \dfrac{\partial ^2{\epsilon_y}}{{\partial {x^2}} }++ \dfrac{\partial ^2{\epsilon_{xy}}} {\partial {x}\partial {y} }++  $$

But what is the other geometrical invant of St. Venant?