Simons cone
In the theory of minimal surfaces, the term is used for the $7$-dimensional cone [ {x_1^2 + x_2^2 + x_3^2 + x_4^2 = x_5^2 + x_6^2 + x_7^2 + x_8^2}subset mathbb R^8, . ] The mean curvature of the Simons' cone vanishes at every point outside the origin: therefore the first variation of the area vanishes along any deformation …