On the Geometry in the Large of Hadamard Manifolds

Abstract

A Hadamard manifold is a simply connected, complete Riemannian manifold with nonpositive sectional curvature. One can find dozens of papers on the geometry in the large of Hadamard manifolds. In the present paper, we prove Liouville-type theorems for conformal, isometric and harmonic pointwise trans-formations of metrics of Hadamard manifolds.