Abstract:In this paper, some properties of F -harmonic and conformal F -harmonic maps between doubly warped product manifolds are studied and new examples of non-harmonic F -harmonic maps are constructed.

In this paper, λ-harmonic maps from a Finsler manifold to a Riemannian manifold are studied. Then, some properties of this kind of harmonic maps are presented and some examples are given. Finally, the stability of the λ-harmonic maps from a Finsler manifold to the standard unit sphere S n (n > 2) is investigated.

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.

No abstract