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Helix surfaces in the Berger sphere

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Abstract

We characterize helix surfaces in the Berger sphere, that is surfaces which form a constant angle with the Hopf vector field. In particular, we show that, locally, a helix surface is determined by a suitable 1-parameter family of isometries of the Berger sphere and by a geodesic of a 2-torus in the 3-dimensional sphere.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy

    Stefano Montaldo

  2. Departamento de Matemática, ICMC/USP-Campus de São Carlos, Caixa Postal 668, 13560-970, São Carlos, SP, Brazil

    Irene I. Onnis

Authors
  1. Stefano Montaldo
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  2. Irene I. Onnis
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Correspondence to Stefano Montaldo.

Additional information

Supported by PRIN 2010-11, Varietà reali e complesse: geometria, topologia e analisi armonica, Italy, N. 2010NNBZ78 003.

Supported by CNPq, Brazil.

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Montaldo, S., Onnis, I.I. Helix surfaces in the Berger sphere. Isr. J. Math. 201, 949–966 (2014). https://doi.org/10.1007/s11856-014-1055-6

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  • DOI: https://doi.org/10.1007/s11856-014-1055-6

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