On the biharmonic and harmonic indices of the Hopf map期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

On the biharmonic and harmonic indices of the Hopf map

Authors:	E Loubeau C Oniciuc

Institution:	Département de Mathématiques, Laboratoire C.N.R.S. U.M.R. 6205, Université de Bretagne Occidentale, 6, Avenue Victor Le Gorgeu, CS 93837, 29238 Brest Cedex 3, France ; Faculty of Mathematics, ``Al.I. Cuza" University of Iasi, Bd. Carol I, no. 11, 700506 Iasi, Romania

Abstract:	Biharmonic maps are the critical points of the bienergy functional and, from this point of view, generalize harmonic maps. We consider the Hopf map $\psi:\mathbb{S}^3\to \mathbb{S}^2$ and modify it into a nonharmonic biharmonic map $\phi:\mathbb{S}^3\to \mathbb{S}^3$ . We show $\phi$ 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.

Keywords:	Harmonic and biharmonic maps Riemannian submersions stability

	点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文