  The steepest descent method for multiobjective optimization on Riemannian
manifolds with lower bounded sectional curvature is analyzed in this paper. The
aim of the paper is twofold. Firstly, an asymptotic analysis of the method is
presented with three different finite procedures for determining the stepsize,
namely, Lipschitz stepsize, adaptive stepsize and Armijo-type stepsize. The
second aim is to present, by assuming that the Jacobian of the objective
function is componentwise Lipschitz continuous, iteration-complexity bounds for
the method with these three stepsizes strategies. In addition, some examples
are presented to emphasize the importance of working in this new context.
Numerical experiments are provided to illustrate the effectiveness of the
method in this new setting and certify the obtained theoretical results.
