Stabilities of \(F\)-stationary maps (Q638737)

For a smooth map \(u: (M,g) \to (N, h)\) between Riemannian manifolds, M. Ara introduced the \(F\)-energy functional \[ E_F (u) = \int_M F\left( \frac{| du |^2 }{2}\right), \] where \(F:[0, \infty) \to [0, \infty)\) is as function of \(C^2\) class; see [\textit{M. Ara}, ``Geometry of \(F\)-harmonic maps'', Kodai Math. J. 22, No. 2, 243--263 (1999; Zbl 0941.58010)]. In this paper, the author discusses the stability with respect to variations on \(M\) of \(F\)-stationary maps, using as \(M\) compact submanifolds of some \(\mathbb{R}^{m+ k}\) or spheres \(S^m\).