A theorem of Hadamard-Cartan type for Kähler magnetic fields

• Adachi Toshiaki

  Department of Mathematics, Nagoya Institute of Technology

Bibliographic Information

Other Title

• A theorem of Hadamard-Cartan type for Kahler magnetic fields
• Essential Killing helices of order less than five on a non-flat complex space form

Abstract

We study the global behavior of trajectories for Kähler magnetic fields on a connected complete Kähler manifold M of negative curvature. Concerning these trajectories we show that theorems of Hadamard-Cartan type and of Hopf-Rinow type hold: If sectional curvatures of M are not greater than c (< 0) and the strength of a Kähler magnetic field is not greater than $¥sqrt{|c|}$, then every magnetic exponential map is a covering map. Hence arbitrary distinct points on M can be joined by a minimizing trajectory for this magnetic field.

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 64 (3), 969-984, 2012

  The Mathematical Society of Japan

Keywords

• Kähler magnetic fields
• trajectories
• trajectory-spheres
• trajectory-harps
• comparison theorem
• theorem of Hopf-Rinow
• theorem of Hadamard-Cartan

Details

• CRID: 1390282680092905856
• NII Article ID: 10031177257
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/06430969
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL BIB ID: 023829487
• Web Site: http://id.ndl.go.jp/bib/023829487
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I023829487
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed