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Constant Angle Surfaces in Lorentzian Berger Spheres

  • Irene I. Onnis
  • Apoena Passos Passamani
  • Paola Piu
Article
  • 42 Downloads

Abstract

In this work, we study helix spacelike and timelike surfaces in the Lorentzian Berger sphere \({\mathbb S}_{\varepsilon }^3\), that is the three-dimensional sphere endowed with a 1-parameter family of Lorentzian metrics, obtained by deforming the round metric on \({\mathbb S}^3\) along the fibers of the Hopf fibration \({\mathbb S}^3\rightarrow {\mathbb S}^2({1}/{2})\) by \(-\varepsilon ^2\). Our main result provides a characterization of the helix surfaces in \({\mathbb S}_{\varepsilon }^3\) using the symmetries of the ambient space and a general helix in \({\mathbb S}_{\varepsilon }^3\), with axis the infinitesimal generator of the Hopf fibers. Also, we construct some explicit examples of helix surfaces in \({\mathbb S}_{\varepsilon }^3\).

Keywords

Helix surfaces Constant angle surfaces Lorentzian Berger sphere 

Mathematics Subject Classification

53B25 53B30 53C40 

Notes

Acknowledgements

The first author was supported by Grant 2016/24707-4, São Paulo Research Foundation (Fapesp). The third author was supported by PRIN 2015 “Varietà reali e complesse: geometria, topologia e analisi armonica” Italy; and GNSAGA-INdAM, Italy.

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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.Departamento de MatemáticaICMC, USPSão CarlosBrazil
  2. 2.Departamento de MatemáticaUFESVitóriaBrazil
  3. 3.Dipartimento di Matematica e InformaticaUniversità degli Studi di CagliariCagliariItaly

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