arXiv subjects

Seyed Mehdi Kazemi Torbaghan

Publications and source records attributed to Seyed Mehdi Kazemi Torbaghan.

2 recordsLinked to original sources

arXiv2022

The Stability of $α-$ Harmonic Maps with Physical Applications

The first result in this study is a non-existence theorem for $α-$harmonic mappings. Additionally, a direct connection between the $α-$ harmonic and harmonic maps is made possible via conformal deformation. Second, the instability of non-constant $α$-harmonic maps is investigated with regard to the target manifold's Ricci curvature requirements. Next, the concept of $α-$stable manifolds and their physical applications are explored. Finally, it is investigated the $α-$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.

math.DG↗

arXiv2022

Existence and Stability of $α-$ harmonic Maps

In this paper, we first study the $α-$energy functional, Euler-Lagrange operator and $α$-stress energy tensor. Second, it is shown that the critical points of $α-$ energy functional are explicitly related to harmonic maps through conformal deformation. In addition, an $α-$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 $α-$ harmonic maps are minimal submanifolds. Then, the stability of any $α-$harmonic map from a Riemannian manifold to a Riemannian manifold with non-positive Riemannian curvature is demonstrated. Finally, the instability of $α-$harmonic maps from a compact manifold to a standard unit sphere is investigated.

math.DG↗