论文标题
通过合理正常曲线具有非常大对称性的矢量分布
Vector distributions with very large symmetries via rational normal curves
论文作者
论文摘要
我们在任何$ n \ geq 7 $上构建一系列等级3分布的顺序，以使其对称群的维度呈$ n $呈指数增长（更准确地说，它等于$ \ propatatorNAMe {fib} _ {fib} _ {n-1}+n+n+n+n+n+n+n $ \ n $ \ n $ \ n $ \ n $ \ n $ \ n $ \ n $ \ bib} fibonacci编号，以$ \ operatatorName {fib} _1 = \ operatatorName {fib} _2 = 1 $），因此确定这些对称性所需的最大加权喷气订单在$ n $中逐渐增长。这些示例与抛物线几何形状形成鲜明对比，在抛物线几何形状相对于环境歧管的尺寸而言，对称群的尺寸在多项式上生长，并且相应的加权射流空间的最大顺序等于基础分布的非单位工程学程度。我们的模型与符号标志的某些曲线和合理正常曲线的几何形状密切相关。
We construct a sequence of rank 3 distributions on $n$-dimensional manifolds for any $n\geq 7$ such that the dimension of their symmetry group grows exponentially in $n$ (more precisely it is equal to $\operatorname{Fib}_{n-1}+n+2$, where $\operatorname{Fib}_n$ is the $n$-th Fibonacci number, starting with $\operatorname{Fib}_1=\operatorname{Fib}_2=1$) and such that the maximal order of weighted jet needed to determine these symmetries grows quadratically in $n$. These examples are in sharp contrast with the parabolic geometries where the dimension of a symmetry group grows polynomially with respect to the dimension of the ambient manifold and the corresponding maximal order of weighted jet space is equal to the degree of nonholonomy of the underlying distribution plus $1$. Our models are closely related to the geometry of certain curves of symplectic flags and of the rational normal curves.
