In this paper, we discuss the geometric properties of solution and lower bound estimate of ∆u m−1 of the Cauchy problem for a degenerate parabolic equation with periodic source term ut = ∆u m +u p sin t. Our objective is to show that: (1) with continuous variation of time t, the surface ϕ = [u(x, t)] mδ q is a complete Riemannian manifold floating in space R N +1 and is tangent to the space R N at ∂H 0 (t); (2) the surface u = u(x, t) is tangent to the hyperplane W (t) at ∂Hu(t).