Constant angle surfaces in Lorentzian Berger spheres

2017/05/29 by Onnis, Irene I., Passamani, Apoena Passos, Piu, Paola · 1 citation
#53B25 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.10090

Abstract

In this work, we study helix spacelike and timelike surfaces in the Lorentzian Berger sphere \s_ε³, that is the three-dimensional sphere endowed with a 1-parameter family of Lorentzian metrics, obtained by deforming the round metric on \s³ along the fibers of the Hopf fibration \s³→ \s²(1/2) by -ε². Our main result provides a characterization of the helix surfaces in \s_ε³ using the symmetries of the ambient space and a general helix in \s_ε³, with axis the infinitesimal generator of the Hopf fibers. Also, we construct some explicit examples of helix surfaces in \s_ε³.

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• Helix surfaces in Lorentzian Heisenberg group

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