A duality for conformally flat hypersurfaces

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• 作者：U. Hertrich-Jeromin ; Y. Suyama ; M. Umehara…
• 关键词：Conformally flat hypersurface ; Combescure transformation ; Guichard dual ; Goursat transformation ; Guichard net ; Ribaucour transformation ; 53C42 ; 53B25 ; 53A30 ; 37K35 ; 37K25
• 刊名：Beitr?ge zur Algebra und Geometrie / Contributions to Algebra and Geometry
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：56
• 期：2
• 页码：655-676
• 全文大小：559 KB
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• 作者单位：U. Hertrich-Jeromin (1)
  Y. Suyama (2)
  M. Umehara (3)
  K. Yamada (4)
  
  1. Technische Universit盲t Wien, E104, Wiedner Hauptstra脽e 8-10, 1040, Wien, Austria
  2. Department of Applied Mathematics, Fukuoka University, Fukuoka, 814-0180, Japan
  3. Department of Mathematics and Computer Sciences, Tokyo Institute of Technology, Tokyo, 152-8552, Japan
  4. Department of Mathematics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra
  Convex and Discrete Geometry
  Geometry
  Algebraic Geometry
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2191-0383

文摘

We discuss the Guichard duality for conformally flat hypersurfaces in a Euclidean ambient space. This duality gives rise to a Goursat-type transformation for conformally flat hypersurfaces, which is generically essential. Using a suitable representation of the associated family of a conformally flat hypersurface in Euclidean space, its dual as well as conformal images of their canonical principal Guichard net(s) are recovered from the family. It is shown that the hypersurface and its dual can be reconstructed from a Ribaucour pair of Guichard nets. Keywords Conformally flat hypersurface Combescure transformation Guichard dual Goursat transformation Guichard net Ribaucour transformation