A duality for conformally flat hypersurfaces
A duality for conformally flat hypersurfaces
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DOI：
10.1007/s13366-014-0225-3
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发表时间：
2014-10
期刊：
影响因子：
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通讯作者：
U. Hertrich-Jeromin;Y. Suyama;M. Umehara;K. Yamada
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文献类型：
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作者：
U. Hertrich-Jeromin;Y. Suyama;M. Umehara;K. Yamada
讨论欧几里得环境空间中共形平面超曲面的Guichard对偶性。这种对偶产生了共形平面超曲面的goursat型变换，这是一般必要的。利用欧几里得空间中共形平面超曲面相关族的合适表示，从族中恢复了它的对偶及其正则主Guichard网的共形象。证明了超曲面及其对偶可以由Ribaucour对Guichard网重构。
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.