The index of biharmonic maps in spheres

By Eric Loubeau, C. Oniciuc. Compositio Mathematica, 2003

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Biharmonic maps are the critical points of the bienergy functional and generalise harmonic maps. We investigate the index of a class of biharmonic maps derived from minimal Riemannian immersions into spheres. This study is motivated by three families of examples: the totally geodesic inclusion of spheres, the Veronese map and the Clifford torus.

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

View Paper: https://www.semanticscholar.org/paper/b19269af3397fa395d36f0db019d45105bc92c83

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

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.”
Some constructions of biharmonic maps and Chen's conjecture on biharmonic hypersurfaces (2009, unknown): “(2) The composition of minimal isometric immersion S( 1 √ 2 ) →֒ S( 1 √ 2 ) followed by the inclusion S( 1 √ 2 ) →֒ S ([6], [19]), the composition of Veronese map: S(2)( √ 3) →֒ S(4)( 1 √ 2 ) →֒ S(5) ([6]); (3) The composition of the Hopf map and the inclusion: S(3)( 1 √ 2 ) −→ S(2)( 1 √ 2 ) →֒ S(3)”
A short survey on biharmonic maps between Riemannian manifolds (2005, background): “Thus the problem is to describe qualitatively their index and nullity. Theorem 9.5 ([ 41 ]).”