A generalization of Hamilton's differential Harnack inequality for the Ricci flow

In [10], R. Hamilton established a differential Harnack inequality for solutions to the Ricci flow with nonnegative curvature operator.We show that this inequality holds under the weaker condition that M × R 2 has nonnegative isotropic curvature. 2tRic ij .Here, Ric and scal denote the Ricci and scalar curvature of (M, g(t)), respectively.Theorem 1. Suppose that (M, g(t)) × R 2 has nonnegative isotropic curvature for all t ∈ (0, T ).