On the biharmonic and harmonic indices of the Hopf map

By Eric Loubeau, C. Oniciuc. 2004

85 citations recorded by the source corpus.

Biharmonic maps are the critical points of the bienergy functional and, from this point of view, generalize harmonic maps. We consider the Hopf map and modify it into a nonharmonic biharmonic map . We show to be unstable and estimate its biharmonic index and nullity. Resolving the spectrum of the vertical Laplacian associated to the Hopf map, we recover Urakawa's determination of its harmonic index and nullity.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/155196aad1e5300e9f4dc1fe3877520471705025

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Some constructions of biharmonic maps and Chen's conjecture on biharmonic hypersurfaces (2009, background): “1 in [18] that the map φ(·, y0) : Sp−1 −→ Sn−1( 1 2) →֒ S n is a proper biharmonic map.”
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.”