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We consider viscosity solutions to nonlinear uniformly parabolic equations innondivergence form on a Riemannian manifold $M$, with the sectional curvaturebounded from below by $-\kappa$ for $\kappa\geq 0$. In the elliptic case, Wangand Zhang \cite{WZ} recently extended the results of \cite{Ca} to nonlinearelliptic equations in nondivergence form on such $M$, where they obtained theHarnack inequality for classical solutions. We establish the Harnack inequalityfor nonnegative {\it viscosity solutions} to nonlinear uniformly {\it parabolicequations} in nondivergence form on $M$.  The Harnack inequality of nonnegative viscosity solutions to the ellipticequations is also proved.

Parabolic Harnack inequality of viscosity solutions on Riemannian manifolds