On the biharmonic and harmonic indices of the Hopf map

• Autores: Eric Loubeau, Cezar Oniciuc
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 11, 2007, págs. 5239-5256
• Idioma: inglés
• DOI: 10.1090/s0002-9947-07-03934-7
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• Resumen

  • 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.