Research on conformally flat hypersurfaces

共形平坦超曲面研究

• 批准号: 21540102
• 负责人: SUYAMA Yoshihiko
• 金额: $ 2.58万
• 依托单位: Fukuoka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540102/
• 关键词: conformally flat; hypersurface; Guichard net; associated family; dual hypersurface; Ribaucour pair; Goursat transformation; conformal flatness; duality; Guichard dual; 共形平坦な超曲面; メービウス幾何; 射影幾何; conformally flat hypersurface; triply orthogonal

We had a great progress in the study on generic conformally flat hypersurfaces of dimension 4. The most important result is that we fund several kinds of transformations between these hypersurfaces. This means that our study on these hypersurfaces made progress to the theory of integral systems for higher dimensional hypersurfaces. Existence of transformations is useful for the construction of new hypersurfaces and for the study toward complete classification of these hypersurfaces: A hypersurface has a one parameter associated family of hypersurfaces. Each hypersurface has a dual hypersurface. We gave an integral formula for the dual. Generally, the members of dual pair are not conformally equivalent, and both duals of a hypersurface and its change by a conformal transformation are also not. There is a one to one correspondence between dual pairs of hypersurfaces and Ribaucour pairs of Guichard nets. We gave an algebraic method for a Guichard net to construct its Ribaucour partner.

我们在四维一般共形平坦超曲面的研究方面取得了很大的进展。最重要的结果是，我们基金之间的这些超曲面的几种变换。这意味着我们对这些超曲面的研究向高维超曲面的积分系统理论迈进了一步。变换的存在性对于构造新的超曲面和研究这些超曲面的完全分类是有用的：一个超曲面有一个单参数的超曲面族。每个超曲面都有一个对偶超曲面。我们给出了对偶的积分公式。一般情况下，对偶对的成员不是共形等价的，超曲面的变换和它的共形变换也不是。对偶超曲面对与Guichard网的Ribaucour对之间存在一一对应关系。给出了Guichard网构造Ribaucour网伙伴的代数方法。

项目成果

Ribaucour pairs corresponding to dual pairs of conformally flat hypersurfaces

对应于双对共形平坦超曲面的里鲍库尔对

• 发表时间: 2014
• 期刊: 福岡大学微分幾何研究会
• 作者: M.Eudave-Munoz;K.Miyazaki;K.Motegi;Shoji Yokura;Kimihiko Motegi and Masakazu Teragaito;Takehiko Yasuda;TERUAKI KITANO;金信泰造;Yukinobu Toda and TakehikoYasuda;Toru Ohmoto;U. Hertrich-Jeromin and Y. Suyama
• 通讯作者: U. Hertrich-Jeromin and Y. Suyama

CONFORMALLY FLAT HYPERSURFACES WITH BIANCHI-TYPE GUICHARD NET

• DOI: 10.18910/24480
• 发表时间: 2013-03
• 期刊: Osaka Journal of Mathematics
• 影响因子: 0.4
• 作者: U. Hertrich-Jeromin;Y. Suyama

Conformally flat hypersurfaces…Existence of an associated family and a dual hypersurface…

共形平坦超曲面……相关族和对偶超曲面的存在……

• 发表时间: 2012
• 期刊: 福岡大学微分幾何研究会2011
• 作者: Hitoshi Furusawa;Koki Nishizawa;Norihiro Tsumagari;Y.Suyama
• 通讯作者: Y.Suyama

共形平坦な超曲面―ある母関数の存在―

共形平坦超曲面 - 某个生成函数的存在性 -

• 发表时间: 2010
• 作者: T.Suzuki;T.Takakura;Takehiko Yasuda;K.Motegi;陶山芳彦
• 通讯作者: 陶山芳彦

福岡大学微分幾何研究会2013報告集

福冈大学微分几何研究组2013年报告集

• 发表时间: 2014
• 作者: 北野晃朗;鈴木正明;K.Motegi;田丸博士;Takehiko Yasuda;Kazuo Akutagawa;辻元;陶山芳彦
• 通讯作者: 陶山芳彦