论文标题
正弯曲和玻色子
Positive curvature and bosons
论文作者
论文摘要
正弯曲和玻色子 紧凑的正曲率riemannian歧管与对称组G相m，可以使conner-kobayashi还原为n，其中n是对称g的固定点集。集合n是较小较小的完全尺寸的完全大地的正曲率歧管，每个曲线均匀均匀。伯杰（Berger），n不是空的。由Lefschetz，M和N具有相同的Euler特征。弗兰克尔（Frankel），n中任意两个组件的维数的总和小于M的维度。将过程n恢复到m的尺寸，可以使用除法代数和地球流量从较小的曲线构建正弯曲歧管。从尺寸6到24，到目前为止，只有四个例外流形出现，其中一些是旗帜歧管，并且在三个维度上与特殊统一组有关。现在，我们可以绘制已知均值均匀曲率歧管的元素的周期系统，并观察到，均匀的已知阳性曲率歧管的列表与物理学中已知的力载体列表具有亲和力。玻色子的正质量与歧管上两个线性独立的谐波K形式的存在相匹配。这促使计算更多的特殊曲率歧管，例如hodge laplacian l = d d*+d* d*+d* d* d* d* d* d*+d* d* d* d* d* d* d* d* d* d* d* d d* d* d* d* d* d d* d* d* d* d* d d* d* d d* d* d d* d d* d* b（u，v）的性能（u，v）属性的最低特殊曲率。
Positive curvature and bosons Compact positive curvature Riemannian manifolds M with symmetry group G allow Conner-Kobayashi reductions M to N, where N is the fixed point set of the symmetry G. The set N is a union of smaller-dimensional totally geodesic positive curvature manifolds each with even co-dimension. By Berger, N is not empty. By Lefschetz, M and N have the same Euler characteristic. By Frankel, the sum of dimension of any two components in N is smaller than the dimension of M. Reverting the process N to M allows to build up positive curvature manifolds from smaller ones using division algebras and the geodesic flow. From dimension 6 to 24, only four exceptional manifolds have appeared so far, some of them being flag manifolds and related to the special unitary group in three dimensions. We can now draw a periodic system of elements of the known even-dimensional positive curvature manifolds and observe that the list of even-dimensional known positive curvature manifolds has an affinity with the list of known force carriers in physics. Positive mass of the boson matches up with the existence of of two linearly independent harmonic k-forms on the manifold. This motivates to compute more quantities of the exceptional positive curvature manifolds like the lowest non-zero eigenvalues of the Hodge Laplacian L=d d*+d* d or properties of the pairs (u,v) of harmonic 2,4 or 8 forms in the positive mass case.
