A generalization of a theorem by Calabi to the parabolic Monge-Ampere equation

We prove that if the function u = u(x, t), convex in x and nonincreasing in t, has time derivative bounded away from 0 and -infinity, and is a solutio n of the parabolic Monge-Ampere equation -u(t)detD(x)(2)u = 1 in R-n x (-in finity,0), then u must be of the form a convex quadratic polynomial in x pl us a linear function of t.