论文标题
关于给定的Jacobi操作员的曲率张量
On the existence of a curvature tensor for given Jacobi operators
论文作者
论文摘要
众所周知，雅各比操作员完全确定了曲率张量。给定的雅各比操作员的存在曲率张量的问题自然会出现，这在先前的工作中被考虑和解决。不幸的是，尽管已发布的定理是正确的，但其证明是不完整的，因为它包含一些遗漏，本文的目的是提供完整而准确的证据。我们还将主要定理概括为无限期标量产品空间的情况。因此，我们概括了Osserman代数曲率张量的比例原理。
It is well known that the Jacobi operators completely determine the curvature tensor. The question of existence of a curvature tensor for given Jacobi operators naturally arises, which is considered and solved in the previous work. Unfortunately, although the published theorem is correct, its proof is incomplete because it contains some omissions, and the aim of this paper is to present a complete and accurate proof. We also generalize the main theorem to the case of indefinite scalar product space. Accordingly, we generalize the proportionality principle for Osserman algebraic curvature tensors.
