The Stability of $\alpha-$ Harmonic Maps with Physical Applications
Differential Geometry
2022-08-26 v1 Mathematical Physics
math.MP
Abstract
The first result in this study is a non-existence theorem for harmonic mappings. Additionally, a direct connection between the harmonic and harmonic maps is made possible via conformal deformation. Second, the instability of non-constant -harmonic maps is investigated with regard to the target manifold's Ricci curvature requirements. Next, the concept of stable manifolds and their physical applications are explored. Finally, it is investigated the stability of compact Riemannian manifolds that admit a non-isometric conformal vector field as well as the Einstein Riemannian manifolds under certain assumption on the smallest positive eigenvalue of its Laplacian operator on functions.
Keywords
Cite
@article{arxiv.2208.11817,
title = {The Stability of $\alpha-$ Harmonic Maps with Physical Applications},
author = {Seyed Mehdi Kazemi Torbaghan and Keyvan Salehi},
journal= {arXiv preprint arXiv:2208.11817},
year = {2022}
}