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

Josef Mikeš (), Vladimir Rovenski and Sergey Stepanov
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Josef Mikeš: Department of Algebra and Geometry, Palacký University Olomouc, 771 47 Olomouc, Czech Republic
Vladimir Rovenski: Department of Mathematics, University of Haifa, Mount Carmel, Haifa 3498838, Israel
Sergey Stepanov: Department of Mathematics, Finance University, 125468 Moscow, Russia

Mathematics, 2022, vol. 10, issue 16, 1-14

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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