  In this paper, we propose nonlinear conjugate gradient methods for vector
optimization on Riemannian manifolds. The concepts of Wolfe and Zoutendjik
conditions are extended for Riemannian manifolds. Specifically, we establish
the existence of intervals of step sizes that satisfy the Wolfe conditions. The
convergence analysis covers the vector extensions of the Fletcher--Reeves,
conjugate descent, and Dai--Yuan parameters. Under some assumptions, we prove
that the sequence obtained by the algorithm can converge to a Pareto stationary
point. Moreover, we also discuss several other choices of the parameter.
Numerical experiments illustrating the practical behavior of the methods are
presented.
