论文标题
Weyl Tensor，强烈规则的图，乘法字符和二次矩阵方程
Weyl Tensors, Strongly Regular Graphs, Multiplicative Characters, and a Quadratic Matrix Equation
论文作者
论文摘要
我们研究riemannian几何形状中产生的二次基质方程的溶液。令$ s $为对角线上的零的真实对称$ n \ times n $ -matrix，让$θ$为真实数字。我们构造了一组二次方程的非零解决方案$（s，θ）$ } i <j。\]我们的解决方案将方程与强量规则图，组环以及有限字段的乘法字符相关联。
We study solutions of a quadratic matrix equation arising in Riemannian geometry. Let $S$ be a real symmetric $n\times n$-matrix with zeros on the diagonal and let $θ$ be a real number. We construct nonzero solutions $(S,θ)$ of the set of quadratic equations \[\sum_kS_{i,k}=0\quad\text{ and }\quad\sum_{k}S_{i,k}S_{k,j}+S_{i,j}^2=θS_{i,j}\text { for }i<j.\] Our solutions relate the equations to strongly regular graphs, to group rings, and to multiplicative characters of finite fields.
