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PERIODIC MINIMAL SURFACES IN SEMIDIRECT PRODUCTS

Part of: Global differential geometry

Published online by Cambridge University Press:  15 October 2013

ANA MENEZES
ANA MENEZES*
Affiliation:
Instituto Nacional de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, 22460-320, Rio de Janeiro-RJ, Brazil email [email protected]
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Abstract

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In this paper we prove the existence of complete minimal surfaces in some metric semidirect products. These surfaces are similar to the doubly and singly periodic Scherk minimal surfaces in ${ \mathbb{R} }^{3} $. In particular, we obtain these surfaces in the Heisenberg space with its canonical metric, and in ${\mathrm{Sol} }_{3} $ with a one-parameter family of nonisometric metrics.

Keywords

semidirect productsminimal surfaces

MSC classification

Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 96 , Issue 1 , February 2014 , pp. 127 - 144
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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