Discrete Projective Differential Geometry: Comprehensive Theory and Integrable Structure

微分几何已经由最杰出的数学家发展了几个世纪，它在数学和物理科学中的适用性是毋庸置疑的。然而，天然建筑和人造建筑本质上都是离散的。离散微分几何是一个相对较新的活跃的研究领域，位于纯数学和应用数学之间，它比微分几何更基础，因为它旨在建立一个独立的离散模拟，从中可以通过适当的连续体极限推导出微分几何。尽管离散微分几何已经达到了高度的复杂程度，但该项目旨在提供该领域的第一个综合理论。

Differential geometry has been developed over centuries by the most distinguished of mathematicians and its applicability in the mathematical and physical sciences is beyond doubt. However, both natural and man-made structures are inherently discrete. Discrete differential geometry constitutes a relatively new and active research area located between pure and applied mathematics which is more fundamental than differential geometry in that it aims to establish an autonomous discrete analogue from which differential geometry may be derived via an appropriate continuum limit. Even though discrete differential geometry has reached a high degree of sophistication, this project seeks to deliver the first comprehensive theory in this area.