2019 # Some Remarks on Bi-f-Harmonic Maps and f-Biharmonic Maps

**Abstract:** In this paper, we prove that the class of bi-f -harmonic maps and that of fbiharmonic maps from a conformal manifold of dimension = 2 are the same (Theorem 1.1). We also give several results on nonexistence of proper bi-f -harmonic maps and f -biharmonic maps from complete Riemannian manifolds into nonpositively curved Riemannian manifolds. These include: any bi-f -harmonic map from a compact manifold into a non-positively curved manifold is f -harmonic (Theorem 1.6), and any f -biharmonic (respectively, bi-f …

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“…Proof. First of all, one sees that y = 0 is a solution of (8). For AC > 0, it is easy to check that (8) has constant solutions y = ± C A .…”

confidence: 94%

“…Proof. First of all, one sees that y = 0 is a solution of (8). For AC > 0, it is easy to check that (8) has constant solutions y = ± C A .…”

confidence: 94%

“…For AC > 0, it is easy to check that (8) has constant solutions y = ± C A . From now on, we only need to consider that y(s) is a nonconstant solution of (8). Putting y = u −1 and substituting this into (8), we obtain…”

confidence: 99%