论文标题
局部分数衍生物对Riemann曲率张量的影响
Effect of local fractional derivatives on Riemann curvature tensor
论文作者
论文摘要
在简短的说明中，我们研究了局部分数衍生物对Riemann曲率张量的影响，这是计算Riemannian歧管曲率的常见工具。为此，首先，我们介绍了一个当地一般的分数衍生词运算符，该操作员将文献中大多数使用的操作员涉及符合，替代性，截断的$ m- $和$ \ MATHCAL {V} - $分数衍生物。然后，根据这个普通运算符，在真实仿射空间$ \ mathbb {r}^{n} $上的特定riemannian公制张量字段与定义的欧几里得一个人不同。联说，我们获得了$ \ mathbb {r}^{n} $ endod wed with tht then terric的riemann曲率张量，即$ 0 $，即本地等距到欧几里得空间。
In this short note, we investigate the effect of the local fractional derivatives on the Riemann curvature tensor that is a common tool in calculating curvature of a Riemannian manifold. For this, first we introduce a general local fractional derivative operator that involves the mostly used ones in the literature as conformable, alternative, truncated $M-$ and $\mathcal{V}-$fractional derivatives. Then, according to this general operator, a particular Riemannian metric tensor field on the real affine space $\mathbb{R}^{n}$ that is different than Euclidean one is defined. In conlusion, we obtain that the Riemann curvature tensor of $\mathbb{R}^{n}$ endowed with this particular metric is identically $0$, namely, locally isometric to Euclidean space.
