arXiv subjects

Keyvan Salehi

Publications and source records attributed to Keyvan Salehi.

3 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↗

arXiv2021

Cohomology Group of $K(\mathbb{Z},4)$ and $K(\mathbb{Z},5)$

We are familiar with properties and structure of topological spaces. One of the powerful tools, which help us to figure out the structure of topological spaces is (Leray- Serre) spectral sequence. Although Eilenberg-Maclane space plays important roles in topology, and respectively geometry. Actually finding cohomology groups of this space can be useful for classifying spaces, and also homotopy groups structure of these groups. This paper discusses how to compute cohomology groups of Eilenberg-Maclane spaces $K(\mathbb{Z}, 4)$ and $K(\mathbb{Z}, 5)$ (cohomology degree less than $11$). Furthermore we give the method to find cohomology groups of $K(\mathbb{Z}, n)$. Some proofs are given to the basic facts about cohomology group of $K(\mathbb{Z}, 5)$ and $K(\mathbb{Z},4).$

math.AT↗