Degeneracy locus of critical points of the distance function on a holomorphic foliation

• Ito Toshikazu

  Department of Natural Science, Ryukoku University

• Scárdua Bruno

  Instituto de Matematica, Universidade Federal do Rio de Janeiro

• Yamagishi Yoshikazu

  Department of Applied Math & Info, Ryukoku University

抄録

We study the geometry of transversality of holomorphic foliations of codimension one in ℂⁿ with spheres, from a viewpoint of dynamics of anti-holomorphic maps in the projective space. A point of non-degenerate contact of a leaf with a sphere is a hyperbolic fixed point of the corresponding dynamics. Around a point of degenerate contact, the intersection of branches of the variety of contacts is described as a bifurcation diagram of a neutral fixed point of dynamics. The Morse index for the distance function from the origin is computed as the complex dimension of an unstable manifold.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

  Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ 66 (1), 123-137, 2014

  一般社団法人 日本数学会

キーワード

• foliation
• singularity
• transversality
• Morse index
• anti-holomorphic

詳細情報

• CRID: 1390001205116359296
• NII論文ID: 130003394349
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/06610123
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL書誌ID: 025162057
• Web Site: http://id.ndl.go.jp/bib/025162057
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I025162057
• 本文言語コード: en
• データソース種別:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可