Abstract and Applied Analysis
Volume 2013 (2013), Article ID 843156, 9 pages
http://dx.doi.org/10.1155/2013/843156
Research Article

Biharmonic Maps and Laguerre Minimal Surfaces

Yusuf Abu Muhanna1 and Rosihan M. Ali2

1Department of Mathematics, American University of Sharjah, P.O. Box 26666, Sharjah, UAE
2School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia

Received 24 October 2012; Accepted 11 March 2013

Academic Editor: Norio Yoshida

Copyright © 2013 Yusuf Abu Muhanna and Rosihan M. Ali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A Laguerre surface is known to be minimal if and only if its corresponding isotropic map is biharmonic. For every Laguerre surface is its associated surface , where lies in the unit disk. In this paper, the projection of the surface associated to a Laguerre minimal surface is shown to be biharmonic. A complete characterization of is obtained under the assumption that the corresponding isotropic map of the Laguerre minimal surface is harmonic. A sufficient and necessary condition is also derived for to be a graph. Estimates of the Gaussian curvature to the Laguerre minimal surface are obtained, and several illustrative examples are given.