Constant Mean Curvature Surfaces and Smoke Ring Flow

恒定平均曲率表面和烟环流

• 批准号: 179877155
• 负责人: Professor Dr. Ulrich Pinkall
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2012-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/179877155?language=en
• 关键词: Constant; Mean; Curvature; Surfaces; Smoke

The Differential Geometry research group at the Department of Mathematics at TU Berlin has been very successful in applying ideas from Differential Geometry to Computer Graphics and using visualization to carry out experiments in Differential Geometry. This led to the development of a new research field in mathematics called Discrete Differential Geometry. Since more than two decades the Differential Geometry research group is having a very successful cooperation with colleagues in particular from China. The aim of this project is to extend this cooperation to the interplay of Discrete Differential Geometry and Computer Graphics. The proposed project consists of three strongly related parts. The first part concerns the extension of our cooperation with leading Differential Geometers in China into the new field of Discrete Differential Geometry and Visualization. The second and central part is a research project on the relation of the theory of surfaces of constant mean curvature and the smoke ring flow of space curves. This concrete research project relies on the interplay of Differential Geometry and Visualization, thus it implements the ideas sketched above and provides a research anchor for other activities within this project. In the third part we want to continue our existing cooperation with leading Differential Geometers in China concerning Geometric Modelling Procedures, Submanifolds and Weyl Geometries.

微分几何研究小组在数学系在TU柏林已经非常成功地应用思想从微分几何计算机图形和使用可视化进行实验微分几何。这导致了一个新的数学研究领域的发展，称为离散微分几何。二十多年来，微分几何研究小组与中国的同事进行了非常成功的合作。这个项目的目的是将这种合作扩展到离散微分几何和计算机图形学的相互作用。拟议的项目包括三个密切相关的部分。第一部分是关于我们与中国领先的微分几何师合作的扩展，进入离散微分几何和可视化的新领域。第二部分是研究常平均曲率曲面理论与空间曲线烟圈流的关系。这个具体的研究项目依赖于微分几何和可视化的相互作用，因此它实现了上面概述的想法，并为该项目中的其他活动提供了研究锚。在第三部分中，我们希望继续我们与中国领先的微分几何师在几何建模过程，子流形和Weyl几何方面的合作。