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.

我们在关于维度4的通用共形扁平性突出的研究中取得了长足的进步。最重要的结果是我们资助了这些超浮标之间的几种转化。这意味着我们对这些高空的研究使整体系统的理论取得了进步，以实现更高维度的曲面。转换的存在对于建造新的Hypersurfaces和针对这些Hypersurfaces的完整分类很有用：Hypersurface具有一个与Hypersurfaces相关的参数家族。每个Hypersurface都有双重脱落表面。我们给出了双重不可或缺的公式。通常，双对的成员在共同的等效上不是同等的，并且两个偶性的双重表面及其通过共形转换的变化也不是。双对曲面和核核对核网对之间有一对一的对应关系。我们为guichard网络提供了一种代数方法来构建其Ribaucour合作伙伴。

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

福岡大学微分幾何研究会2010

福冈大学微分几何研究组 2010

• 发表时间: 2010
• 作者: Jorg Schtlrmann;Shoji Yokura;Kazuo Akutagawa;小池直之;中川征樹;陶山芳彦;高倉樹;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