论文标题
几何形状破裂
Symmetry breaking in geometry
论文作者
论文摘要
几何机制可能类似于物理学的类似概念，被认为是几何形状中的“对称性破坏”，并且讨论了这种机制在差异几何形状中的几个实例：它显示出可能发生自发对称性破坏，并讨论了如何使用显式对称性破裂来解决某些角度的问题。提出了对几何形状中对称性破裂的系统研究，并制定了一些对进一步研究的初步思想。
A geometric mechanism that may, in analogy to similar notions in physics, be considered as "symmetry breaking" in geometry is described, and several instances of this mechanism in differential geometry are discussed: it is shown how spontaneous symmetry breaking may occur, and it is discussed how explicit symmetry breaking may be used to tackle certain geometric problems. A systematic study of symmetry breaking in geometry is proposed, and some preliminary thoughts on further research are formulated.
