On the geometry in the large of Hadamard manifolds

Sergey Stepanov, Irina Tsyganok

A Hadamard manifold is a simply connected, complete Riemannian manifold with nonpositive sectional curvature. The theory of Hadamard manifolds is a topic that has been more and more intensively studied for more than forty years. In the present paper, we prove Liouville-type theorems for conformal, isometric and harmonic pointwise transformations of metrics of Hadamard manifolds.