Minkowski空间中伪零增长曲面的几何结构

Geometric Structure of Pseudo Null Growth Surfaces in Minkowski Space

自然界中很多生物的生长过程在数学中可以理解为曲面的增长,即质量在物体表面的沉积,如贝壳、鹿角等.为了探索生物体表面生长过程的多样性,本文在Minkowski空间中定义并研究由伪零曲线作为生成曲线,并按照给定的生长速度及其方向演化而生成的伪零增长曲面.利用伪零曲线的结构函数探索伪零增长曲面的几何结构,并考虑由伪零螺线生成的增长曲面的几何结构表达式,同时辅以典型的例子来明确地刻画此类增长曲面的生成过程.

The growth process of many biological beings in nature can be explained by the surface growth in mathematics,that is,the deposition of mass on the surface of objects,such as shells,antlers and so on.In order to explore the diversity of the growth process on the surface of biological beings,we would define and study the pseudo null growth surface generated by pseudo null curve according to denoted direction and growth velocity in Minkowski 3-space.Meanwhile,the geometric structure of the pseudo null growth surface is analyzed by the aid of the structure function of the generating pseudo null curve,and the expression form of pseudo null growth surface evolved by the pseudo null helices is studied.In addition,several typical examples are designed to explicitly characterize the generation process of such growth surfaces.