On Ribaucour transformations for surfaces
主 题: On Ribaucour transformations for surfaces
报告人: KETI TENENBLAT (巴西利亚大学，巴西科学院院士，第三世界科学院院士)
时 间: 2014-10-20 8:00-9:30
地 点: 理科一号楼1570（主持人：莫小欢）
We consider Ribaucour transformations for linear Weingarten surfaces in space forms. We show that such a transformation is a Darboux transformation iff the surfaces have same constant mean curvature, and such transformations for minimal surfaces in R3 produce embedded planar ends while for cmc1 surfaces immersed in H3 are embedded ends of horosphere type. We prove that the Lawson correspondence commutes with the Darboux transformations, and the property of completeness is preserved by this commutativity. Applications of these results give families of explicitly parametrized complete surfaces with any finite or finite number of planar ends, bubbles, and “segments" or embedded ends of horosphere type. Related applications for flat surfaces and PDEs will also be given. Many surfaces will be visualized by computer graphics.