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Pseudo-parallel surfaces of \(\mathbb {S}_c^n \times \mathbb {R}\) and \(\mathbb {H}_c^n \times \mathbb {R}\)

  • G. A. LobosEmail author
  • M. P. Tassi
  • A. J. Yucra Hancco
Article
  • 49 Downloads

Abstract

In this work we give a characterization of pseudo-parallel surfaces in \(\mathbb {S}_c^n \times \mathbb {R}\) and \(\mathbb {H}_c^n\times \mathbb {R}\), extending an analogous result by Asperti-Lobos-Mercuri for the pseudo-parallel case in space forms. Moreover, when \(n=3\), we prove that any pseudo-parallel surface has flat normal bundle. We also give examples of pseudo-parallel surfaces which are neither semi-parallel nor pseudo-parallel surfaces in a slice. Finally, when \(n\ge 4\) we give examples of pseudo-parallel surfaces with non vanishing normal curvature.

Keywords

Surface Parallel Semi-parallel Pseudo-parallel \(\lambda \)-Isotropic Minimal 

Mathematics Subject Classification

53B25 53C42 

Notes

Acknowledgements

The authors are thankful to the referee for their valuable comments and suggestions towards the improvement of this work.

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Copyright information

© Sociedade Brasileira de Matemática 2018

Authors and Affiliations

  1. 1.Departament of MathematicsFederal University of São CarlosSão CarlosBrazil
  2. 2.Federal University of TocantinsCampus AraguaínaAraguaínaBrazil

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