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Contact real hypersurfaces in the complex hyperbolic quadric

  • Sebastian KleinEmail author
  • Young Jin Suh
Article

Abstract

We discuss the geometry of contact real hypersurfaces with constant mean curvature in the complex hyperbolic quadric \({Q^m}^* = SO_{m,2}^o/SO_mSO_2\), where \(m\ge 3\). These hypersurfaces were classified in Berndt and Suh (Proc Am Math Soc 143:2637–2649, 2015), and we study the individual types (two types of tubes around totally geodesic submanifolds of  \({Q^m}^*\) and one type of horosphere) that have been found in that classification.

Keywords

Contact hypersurface Kähler structure Complex conjugation Complex hyperbolic quadric 

Mathematics Subject Classification

Primary 53C40 Secondary 53C55 

Notes

Acknowledgements

This work was done while Sebastian Klein was visiting professor at the Research Institute of Real and Complex Submanifolds in Kyungpook National University during October, 2017.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Fakultät für Wirtschaftsinformatik und WirtschaftsmathematikUniversität MannheimMannheimGermany
  2. 2.Department of Mathematics & RIRCM, College of Natural SciencesKyungpook National UniversityDaeguRepublic of Korea

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