On Harmonic and Asymptotically Harmonic Finsler Manifolds
Abstract
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 -curvature.
Keywords
Cite
@article{arxiv.2005.03616,
title = {On Harmonic and Asymptotically Harmonic Finsler Manifolds},
author = {Hemangi Shah and Ebtsam H. Taha},
journal= {arXiv preprint arXiv:2005.03616},
year = {2024}
}
Comments
The initial version v2 has been divided in to two articles. The first article is the present version (which concerns with the first five sections of v2) 24 pages, 4 tables. The second article (by the same authors) will be submitted separately to arXiv very soon