Riemannian manifolds admitting a projective vector field
Riemannian manifolds admitting a projective vector field
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黎曼流形承认射影向量场
DOI：
10.2996/kmj/1138036262
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发表时间：
1980
影响因子：
0.6
通讯作者：
H. Hiramatu
中科院分区：
文献类型：
--
作者：
H. Hiramatu
设 M 为由坐标邻域系统 {U x} 覆盖的维度为 n 的连通黎曼流形，其中，此处和后续的索引 h, i, j , k,••• 在范围 {1, 2,•••, n) 上运行，并令 gjif {/J, V 3, Kkji , Kji 和 K 分别为度量张量，由 gji 形成的 Christoffel 符号，gji 是关于{/*}、曲率张量、Ricci 张量和 M 的标量曲率。M 上的向量场 v 称为射影向量场，如果满足
Let M be a connected Riemannian manifold of dimension n covered by a system of coordinate neighborhoods {U x}, where, here and in the sequel, the indices h, i, j , k, ••• run over the range {1, 2, •••, n) and let gjif {/J, V 3, Kkji , Kji and K be respectively the metric tensor, the Christoffel symbols formed with gji, the operator of covariant differentiation with respect to {/*}, the curvature tensor, the Ricci tensor and the scalar curvature of M. A vector field v on M is called a projective vector field if it satisfies