A theorem of Hadamard-Cartan type for Kähler magnetic fields

DOI10.2969/jmsj/06430969zbMath1252.53047OpenAlexW2095295322MaRDI QIDQ455014

Toshiaki Adachi

Publication date: 2 October 2012

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jmsj/1343133751

zbMATH Keywords

trajectoriescomparison theoremKähler magnetic fieldstrajectory-spherestheorem of Hadamard-Cartantheorem of Hopf-Rinowtrajectory-harps

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Local differential geometry of Hermitian and Kählerian structures (53B35)

Related Items

Foliation on the moduli space of extrinsic circular trajectories on a complex hyperbolic space, Accurate trajectory-harps for Kähler magnetic fields, Asymptotic behaviors of trajectories on a Hadamard Kähler manifold, Kähler magnetic fields on Kähler manifolds of negative curvature, An estimate on volumes of trajectory-balls for Kähler magnetic fields, Distances from unbounded trajectories to their limit-strings on a Hadamard Kähler manifold, Volumes of trajectory-balls for Kähler magnetic fields, Estimates on arc-lengths of trajectory-fronts for surface magnetic fields

Cites Work

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• The theorem of E. Hopf under uniform magnetic fields
• Magnetic flows of Anosov type
• Kähler magnetic flows for a manifold of constant holomorphic sectional curvature
• On circles and spheres in Riemannian geometry
• A comparison theorem on magnetic jacobi fields
• MAGNETIC JACOBI FIELDS FOR KÄHLER MAGNETIC FIELDS