On biharmonic maps

By R. Caddeo, Stefano Montaldo, M. Piu. 2001

87 citations recorded by the source corpus.

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Biharmonic Submanifolds in a Riemannian Manifold with Non-Positive Curvature (2011, unknown): “A C map φ : (M, g) → (N, h) is called to be biharmonic ([2], [5], [7]) if τ2(φ) = 0.”
A short survey on biharmonic maps between Riemannian manifolds (2005, unknown): “For more examples see [14, 15].”
Some constructions of biharmonic maps and Chen's conjecture on biharmonic hypersurfaces (2009, background): “x(2)1 + x 2 2 , x3) and a certain conformally flat metric ḡ ([27]); (iii) Biharmonic Riemannian submersions [20]: φ : (R(2) × R, dx(2) + dy(2) + β(2)(x)dz(2)) → (R(2), dx(2) + dy(2)), φ(x, y, z) = (x, y) with c1, c2 ∈ R∗, β = c2 e R f(x) , and f(x) = −c1(1+e 1) 1−ec1x , is a family of biharmonic Rie”
Biharmonic maps into a Riemannian manifold of non-positive curvature (2012, background): “Jiang [15] studied the first and second variation formulas of E2, extensive studies in this area have been done (for instance, see [2], [4], [18], [19], [21], [24], [26], [12], [13], [14], etc.”