Small, Anthony (1999) Duality for a class of minimal surfaces in Rn+1. Tohoku Mathematical Journal, 51 (4). pp. 585-601. ISSN 0040-8735

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Abstract

Much is known about the geometry of a minimal surface in Euclidean space whose Gauss map takes values on a linear subspace of the quadric hypersurface. We consider minimal surfaces whose Gauss maps take values on rational normal curves. These are the non-degenerate minimal surfaces with smallest possible Gaussian images. We show that the geometry of such a minimal surface may be understood in terms of an auxiliary holomorphic curve on the total space of a line bundle over the Gaussian image. This is related to classical osculation duality. Natural analogues in higher dimensions of Enneper's surface, Henneberg's surface and surfaces with Platonic symmetries are described in terms of algebraic curves.

Item Type:	Article
Keywords:	Duality; minimal surfaces; Rn+1;
Academic Unit:	Faculty of Science and Engineering > Mathematics and Statistics
Item ID:	10101
Depositing User:	Dr. Anthony Small
Date Deposited:	15 Oct 2018 17:24
Journal or Publication Title:	Tohoku Mathematical Journal
Publisher:	Tohoku University, Mathematical Institute
Refereed:	Yes
URI:
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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