  We study viscosity solutions to degenerate and singular elliptic equations of
$p$-Laplacian type on Riemannian manifolds. The Krylov-Safonov type Harnack
inequality for the $p$-Laplacian operators with $1<p<\infty$ is established on
the manifolds with Ricci curvature bounded from below based on ABP type
estimates. We also prove the Harnack inequality for nonlinear $p$-Laplacian
type operators assuming that a nonlinear perturbation of Ricci curvature is
bounded below.
