A Contribution of Liouville-Type Theorems to the Geometry in the Large of Hadamard Manifolds

Abstract

A complete, simply connected Riemannian manifold of nonpositive sectional curvature is called a Hadamard manifold. In this article, we prove Liouville-type theorems for isometric and harmonic self-diffeomorphisms of Hadamard manifolds, as well as Liouville-type theorems for Killing–Yano, symmetric Killing and harmonic tensors on Hadamard manifolds.

Keywords

• Hadamard manifold
• subharmonic, harmonic and convex functions
• isometric and harmonic diffeomorphisms
• Killing and harmonic tensors