Geometry of generalized F-harmonic maps

Abstract

In this paper, we extend the definition of F-harmonic maps [1] and, we give the notion of F-biharmonic maps, which is a generalization of biharmonic maps between Riemannian manifolds [3] and f-biharmonic maps [7] and we discuss some conformal properties and the stability of F-harmonic maps. Also, we give a formula to construct some examples of proper Fbiharmonic maps. Our results are extensions of [1] and [7].

Existence and Stability of α−Harmonic Maps

“…Furthermore, in [10], it is studied the energy identity and necklessness for a sequence of Sacks-Uhlenbeck maps during blowing up. Following the concepts of [1,4,[8][9][10][11][12][13][14], we study the stability, existence, and structure of α-harmonic maps, as well as their practical applications, in this work. e existence of α− harmonic maps in an arbitrary class of homotopy and the conditions under which the fibers of α− harmonic maps are minimal submanifolds are explored in particular.…”