On the rigidity theorems for lagrangian translating solitons in pseudo-Euclidean space I

Let f be a smooth strictly convex solution of det(.2f.xi.xj)=exp{.i=1n.ai.f.xi+.i=1nbixi+c} defined on a domain . . .n, where a i , b i and c are constants, then the graph M .f of .f is a spacelike translating soliton for mean curvature flow in pseudo-Euclidean space . 2nn with the translating vector 1n (a 1, a 2, ., a n ; b 1, b 2, ., b n ). In this paper, we will use affine technique to show a Bernstein Theorem: if the graph M .f is complete, then f(x) must be a quadratic polynomial and M .f is an affine n-plane.