Pseudo-Spherical Submanifolds with 1-Type Pseudo-Spherical Gauss Map

Burcu Bektaş, Elif Özkara Canfes, Uğur Dursun*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

In this work, we study pseudo-Riemannian submanifolds of a pseudo-sphere with 1-type pseudo-spherical Gauss map. First, we classify Lorentzian surfaces in a 4-dimensional pseudo-sphere Ss4(1) with index s, s= 1 , 2 , and having harmonic pseudo-spherical Gauss map. Then we give a characterization theorem for pseudo-Riemannian submanifolds of a pseudo-sphere Ssm-1(1)⊂Esm with 1-type pseudo-spherical Gauss map, and we classify spacelike surfaces and Lorentzian surfaces in the de Sitter space S14(1)⊂E15 with 1-type pseudo-spherical Gauss map. Finally, according to the causal character of the mean curvature vector we obtain the classification of submanifolds of a pseudo-sphere having 1-type pseudo-spherical Gauss map with nonzero constant component in its spectral decomposition.

Original languageEnglish
Pages (from-to)867-887
Number of pages21
JournalResults in Mathematics
Volume71
Issue number3-4
DOIs
Publication statusPublished - 1 Jun 2017

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing.

Keywords

  • biharmonic Gauss map
  • Finite type mapping
  • marginally trapped surface
  • pseudo-sphere
  • pseudo-spherical Gauss map

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