Darboux curves on surfaces(1)

• Garcia Ronaldo

  Instituto de Matemática e Estatística, Universidade Federal de Goiás

• Langevin Rémi

  Institut de Mathématiques de Bourgogne, UMR CNRS 5584, Université de Bourgogne Franche-Comté

• Walczak Paweł

  Katedra Geometrii, Wydział Matematyki i Informatyki, Uniwersytet Łódzki

書誌事項

タイトル別名

• Darboux curves on surfaces I

抄録

In 1872, G. Darboux defined a family of curves on surfaces of ℝ³ which are preserved by the action of the Möbius group and share many properties with geodesics. Here, we characterize these curves under the view point of Lorentz geometry and prove that they are geodesics in a 3-dimensional sub-variety of a quadric Λ⁴ contained in the 5-dimensional Lorentz space ℝ⁵₁ naturally associated to the surface. We construct a new conformal object: the Darboux plane-field 𝒟 and give a condition depending on the conformal principal curvatures of the surface which guarantees its integrability. We show that 𝒟 is integrable when the surface is a special canal.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

  Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ 69 (1), 1-24, 2017

  一般社団法人 日本数学会

キーワード

• Darboux curves
• conformal geometry
• space of spheres

詳細情報

• CRID: 1390001205115605376
• NII論文ID: 130005310388
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/06910001
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL書誌ID: 027858973
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I027858973
• 本文言語コード: en
• データソース種別:
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