We give some sufficient conditions for stochastically complete Riemannian manifolds with parallel Cotton tensor to be either Einstein or of constant sectional curvature, and obtain an optimal pinching theorem. In particular, when $n$ = 4, we give a full classification.
"Some remarks on Riemannian manifolds with parallel Cotton tensor." Kodai Math. J. 42 (1) 64 - 74, March 2019. https://doi.org/10.2996/kmj/1552982506