CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Helicoidal Minimal Surfaces in a Finsler Space of Randers Type

  • Rosângela Maria da Silva,
    Instituto de Matemática e Estatística, IME-Universidade Federal de Goiás, 74001-970, Goiânia, GO, Brazil
  • Keti Tenenblat,
    Departamento de Matemática, Universidade de Brasília, 70904-970, Brasília, DF, Brazil
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   LaTeX   MathJax   PDF  

Abstract

We consider the Finsler space $(\bar{M}^3, \bar{F})$ obtained by perturbing the Euclidean metric of $\mathbb{R}^3$ by a rotation. It is the open region of $\mathbb{R}^3$ bounded by a cylinder with a Randers metric. Using the Busemann-Hausdorff volume form, we obtain the differential equation that characterizes the helicoidal minimal surfaces in $\bar{M}^3$. We prove that the helicoid is a minimal surface in $\bar{M}^3$, only if the axis of the helicoid is the axis of the cylinder. Moreover, we prove that, in the Randers space $(\bar{M}^3, \bar{F})$, the only minimal surfaces in the Bonnet family, with fixed axis $O\bar{x}^3$, are the catenoids and the helicoids.
Keywords: minimal surfaces, helicoidal surfaces, Finsler space, Randers space minimal surfaces, helicoidal surfaces, Finsler space, Randers space
MSC Classifications: 53A10, 53B40 show english descriptions Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Finsler spaces and generalizations (areal metrics)
53A10 - Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
53B40 - Finsler spaces and generalizations (areal metrics)
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/