“…So, currently, one priority and a practical thing to do seems to be finding more examples of proper biharmonic maps between certain model spaces or studying biharmonic maps under some geometric constraints. For example, one can study biharmonic isometric immersions which lead to the concept of biharmonic submanifolds (see e.g., [11], [6], [7], [4], [5], [15] and [3]); one can also study, as in [1], [2], [14], horizontally weakly conformal biharmonic maps which generalize both the notion of harmonic morphisms (maps that are both horizontally weakly conformal and harmonic) and that of biharmonic morphisms (maps that are horizontally weakly conformal biharmonic with other constraints, see [16], [13], [17], and [14] for details).…”