论文标题
限制完整投影特殊真实歧管的几何形状
Limit geometry of complete projective special real manifolds
论文作者
论文摘要
我们研究完整的射影特殊真实歧管的极限几何形状。按极限几何形状，我们的意思是沿着某些曲线的定义多项式和质心基本形式的演变的极限，这些曲线留下了初始完整的特殊特殊实际歧管的每个紧凑子集。我们获得了可能的极限几何形状列表，这些几何形状本身就是完整的特殊真实歧管，并为其各自的对称组的维度找到了下限。我们进一步表明，如果初始歧管具有规则的边界行为，则每个可能的极限几何形状都是同构对$ \ Mathbb {r} _ {> 0} \ ltimes \ Mathbb {r}^{n-1} $。
We study the limit geometry of complete projective special real manifolds. By limit geometry we mean the limit of the evolution of the defining polynomial and the centro-affine fundamental form along certain curves that leave every compact subset of the initial complete projective special real manifold. We obtain a list of possible limit geometries, which are themselves complete projective special real manifolds, and find a lower bound for the dimension of their respective symmetry groups. We further show that if the initial manifold has regular boundary behaviour, every possible limit geometry is isomorphic to $\mathbb{R}_{>0}\ltimes\mathbb{R}^{n-1}$.
