Existence and Stability of α−Harmonic Maps

Seyed Mehdi Kazemi Torbaghan, Keyvan Salehi, Salman Babayi and Rafael López

Journal of Mathematics, 2022, vol. 2022, 1-10

Abstract: 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 the 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 on Riemannian manifold with nonpositive curvature is studied. Finally, the instability of α−harmonic maps from a compact manifold to a standard unit sphere is investigated.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:1906905

DOI: 10.1155/2022/1906905

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