论文标题
在三维谎言组上的广义爱因斯坦指标的分类
Classification of generalized Einstein metrics on 3-dimensional Lie groups
论文作者
论文摘要
我们在谎言群体上发展了左旋不变的普遍伪里曼尼亚人指标的理论。这样的度量标准伴随着左右发散操作员的选择会产生RICCI曲率张量，我们研究相应的爱因斯坦方程。我们根据编码Courant Algebroid结构的张量（按LIE代数及其双重）计算RICCI张量，该张量，通用度量标准和分歧运算符。所得的表达是多项式和均匀的二级表达在Dorfman支架的系数中，而发散算子则相对于广义度量的剩余不变的正常基础。我们确定了三维谎言组的所有广义爱因斯坦指标。
We develop the theory of left-invariant generalized pseudo-Riemannian metrics on Lie groups. Such a metric accompanied by a choice of left-invariant divergence operator gives rise to a Ricci curvature tensor and we study the corresponding Einstein equation. We compute the Ricci tensor in terms of the tensors (on the sum of the Lie algebra and its dual) encoding the Courant algebroid structure, the generalized metric and the divergence operator. The resulting expression is polynomial and homogeneous of degree two in the coefficients of the Dorfman bracket and the divergence operator with respect to a left-invariant orthonormal basis for the generalized metric. We determine all generalized Einstein metrics on three-dimensional Lie groups.
