论文标题
两根riemannian歧管
Two-root Riemannian Manifolds
论文作者
论文摘要
Osserman歧管是局部两点均匀空间的概括。我们介绍了$ k $ - 根歧管，其中减少的雅各比运营商具有$ k $ eigenvalues。我们将单根和两根歧管研究作为局部两点均匀空间的另一个概括。我们证明没有奇数维度的两根riemannian歧管。在两倍的奇数维度中，我们描述了所有两根riemannian代数曲率张量，并为双根riemannian歧管提供了其他条件。
Osserman manifolds are a generalization of locally two-point homogeneous spaces. We introduce $k$-root manifolds in which the reduced Jacobi operator has exactly $k$ eigenvalues. We investigate one-root and two-root manifolds as another generalization of locally two-point homogeneous spaces. We prove that there is no two-root Riemannian manifold of odd dimension. In twice an odd dimension, we describe all two-root Riemannian algebraic curvature tensors and give additional conditions for two-root Riemannian manifolds.
