论文标题
riemannian流形的代数特性
Algebraic Properties of Riemannian Manifolds
论文作者
论文摘要
使用曲率张量的不可约合分解，探索了Riemannian歧管的曲率张量的代数特性。我们的方法提供了一种强大的工具来分析不可约理基的基础和算法，以确定任意riemann多项式的线性依赖性。我们完全为四分之一标量指定了13个独立的基础元素，并明确地找到了26个标量不变的13个线性关系。我们的方法提供了几个全新的结果，包括一些线索，这些线索可以从90个五重量标量中识别23个独立的基础元素，而这些元素很难找到。
Algebraic properties are explored for the curvature tensors of Riemannian manifolds, using the irreducible decomposition of curvature tensors. Our method provides a powerful tool to analyze the irreducible basis as well as an algorithm to determine the linear dependence of arbitrary Riemann polynomials. We completely specify 13 independent basis elements for the quartic scalars and explicitly find 13 linear relations among 26 scalar invariants. Our method provides several completely new results, including some clues to identify 23 independent basis elements from 90 quintic scalars, that are difficult to find otherwise.
