Manifolds whose curvature operator has constant eigenvalues at the basepoint
Manifolds whose curvature operator has constant eigenvalues at the basepoint
复制标题
曲率算子在基点具有恒定特征值的流形
DOI：
--
复制
发表时间：
1994
期刊：
影响因子：
--
通讯作者：
P. Gilkey
中科院分区：
文献类型：
--
作者：
P. Gilkey
Osserman证明了如果黎曼流形M的曲率算子R具有常特征值，则M是局部秩1对称空间或平坦空间.这个问题要复杂得多。我们给出了黎曼流形的例子，使得R在基点上有常特征值，但R不是秩-1对称空间的曲率算子。
Osserman conjectured that if the curvature operatorR of a Riemannian manifoldM has constant eigenvalues, thenM is locally a rank-1 symmetric space or is flat. The pointwise question is considerably more complicated. We present examples of Riemannian manifolds so thatR has constant eigenvalues at the basepoint, butR is not the curvature operator of a rank-1 symmetric space.