Existence and Stability of $\alpha-$ harmonic Maps
Differential Geometry
2022-08-18 v1 Mathematical Physics
math.MP
Abstract
In this paper, we first study the energy functional, Euler-Lagrange operator and -stress energy tensor. Second, it is shown that the critical points of energy functional are explicitly related to harmonic maps through conformal deformation. In addition, an harmonic map is constructed from any smooth map between Riemannian manifolds under certain assumptions. Next, we determine the conditions under which the fibers of horizontally conformal harmonic maps are minimal submanifolds. Then, the stability of any harmonic map from a Riemannian manifold to a Riemannian manifold with non-positive Riemannian curvature is demonstrated. Finally, the instability of harmonic maps from a compact manifold to a standard unit sphere is investigated.
Cite
@article{arxiv.2208.07995,
title = {Existence and Stability of $\alpha-$ harmonic Maps},
author = {Seyed Mehdi Kazemi Torbaghan and Keyvan Salehi and Salman Babayi},
journal= {arXiv preprint arXiv:2208.07995},
year = {2022}
}