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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Josef Mikeš & Vladimir Rovenski & Sergey Stepanov, 2022. "A Contribution of Liouville-Type Theorems to the Geometry in the Large of Hadamard Manifolds," Mathematics, MDPI, vol. 10(16), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2880-:d:886065
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