Critical Points of the Distance Function on the Moduli Space for Spherical Eigenmaps and Minimal Immersions
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چکیده
The boundary of a DoCarmo-Wallach moduli space parametrizing (harmonic) eigenmaps between spheres or spherical minimal immersions carries a natural stratification. In this paper we study the critical points of the distance function on the boundary strata. We show that the critical points provide a natural generalization of eigenmaps with L-orthonormal components. We also point out that many classical examples of eigenmaps correspond to critical points. MSC 2000: 53C42, 58E20
منابع مشابه
Moduli for Spherical Eigenmaps and Minimal Immersions
Eigenmaps and spherical minimal immersions of round spheres into round spheres form an interesting subject that has been studied by many authors. The components of an eigenmap are eigenfunctions of the Laplace-Beltrami operator on Sm, the Euclidean m-sphere, m ≥ 2; and the eigenfunctions correspond to a fixed eigenvalue λk, k ≥ 1. Given m ≥ 2 and k ≥ 1, these eigenmaps can be parametrized by a ...
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تاریخ انتشار 2004