论文标题
关于谐波和渐近谐波鳍片
On Harmonic and Asymptotically Harmonic Finsler Manifolds
论文作者
论文摘要
在本文中，我们介绍并研究了各种类型的谐波鳍歧管，并找出它们之间的相互关系。我们从大地球体的平均曲率和鳍式结构引起的距离函数的拉普拉曲板的平均曲率方面给出了一些特征。我们研究了不同半径的芬斯勒平均曲率的某些特性。此外，我们证明某些谐波鳍片是爱因斯坦类型的，并提供了一种构建Randers类型的谐波鳍歧管的技术。此外，我们举了一些恒定标志曲率和恒定$ s $ curvature的非里姆人鳍谐音歧管的例子。
In the present paper, we introduce and investigate various types of harmonic Finsler manifolds and find out the interrelation between them. We give some characterizations of such spaces in terms of the mean curvature of geodesic spheres and the Laplacian of the distance function induced by the Finsler structure. We investigate some properties of the Finsler mean curvature of geodesic spheres of different radii. In addition, we prove that certain harmonic Finsler manifolds are of Einstein type and provide a technique to construct harmonic Finsler manifolds of Randers type. Moreover, we give some examples of non-Riemmanian Finsler harmonic manifolds of constant flag curvature and constant $S$-curvature.
