Length spectrum of geodesic spheres in a non-flat complex space form

• ADACHI Toshiaki

  Department of Mathematics Nagoya Institute of Technology

• MAEDA Sadahiro

  Department of Mathematics Shimane University

• YAMAGISHI Masakazu

  Department of Mathematics Nagoya Institute of Technology

Abstract

We investigate the distribution of length of closed geodesics on geodesic spheres and tubes around complex hyperplane in a non-flat complex space form. The feature of the length spectrum of a geodesic sphere of radius r in a complex projec-tive space of holomorphic sectional curvature 4 is quite different according as tan²r is rational or irrational. Each length spectrum is simple when tan²r is irrational, but when tan²r is rational, it is not necessarily simple and moreover the multiplicity is not uniformly bounded.

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 54 (2), 373-408, 2002

  The Mathematical Society of Japan

Keywords

• geodesic sphere
• length spectrum
• real hypersurfaces
• complex space form

Details

• CRID: 1390282680091085440
• NII Article ID: 10008205005
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/05420373
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• MRID: 1883524
• NDL BIB ID: 6153530
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I6153530
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed