论文标题
在标量曲率和衡量性的喷雾剂上
On Sprays of Scalar Curvature and Metrizability
论文作者
论文摘要
每个Finsler指标自然都会诱发喷雾，但并非如此。标量（各向同性）曲率喷雾剂的概念被称为标量标量（各向同性）标志性标志曲率曲率的概括。在本文中，引入了一个新的概念，即恒定曲率的喷雾，尤其是表明，即使在尺寸$ n \ ge3 $中，各向同性曲率的喷雾也不一定是恒定曲率。此外，给出了各向同性（恒定）曲率喷雾剂的完整条件，为Finsler-Metrizabile。由于这种结果的应用，确定了局部结构的局部局部结构，该局部结构是在局部的弯曲（分别恒定）曲率的曲线，这些曲率是Finsler-oterizable的，并且还讨论了更多的各向同性曲率的喷雾剂。此外，在某些曲率条件下，还研究了标态曲率喷雾剂的衡量性问题。
Every Finsler metric naturally induces a spray but not so for the converse. The notion for sprays of scalar (resp. isotropic) curvature has been known as a generalization for Finsler metrics of scalar (resp. isotropic) flag curvature. In this paper, a new notion, sprays of constant curvature, is introduced and especially it shows that a spray of isotropic curvature is not necessarily of constant curvature even in dimension $n\ge3$. Further, complete conditions are given for sprays of isotropic (resp. constant) curvature to be Finsler-metrizabile. As applications of such a result, the local structure is determined for locally projectively flat Berwald sprays of isotropic (resp. constant) curvature which are Finsler-metrizable, and some more sprays of isotropic curvature are discussed for their metrizability. Besides, the metrizability problem is also investigated for sprays of scalar curvature under certain curvature conditions.
