Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 1, pp. 305-328 (2004)
Critical points of the distance function on the moduli space for spherical eigenmaps and minimal immersions
Gabor TothDepartment of Mathematics, Rutgers University, Camden, New Jersey 08102; e-mail: firstname.lastname@example.org
Abstract: 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 $L^2$-orthonormal components. We also point out that many classical examples of eigenmaps correspond to critical points.
Classification (MSC2000): 53C42, 58E20
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Electronic version published on: 5 Mar 2004. This page was last modified: 4 May 2006.