Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Contact hypersurfaces in Kähler manifolds

Authors: Jürgen Berndt and Young Jin Suh
Journal: Proc. Amer. Math. Soc. 143 (2015), 2637-2649
MSC (2010): Primary 53D10; Secondary 53C40, 53C55
Published electronically: February 16, 2015
MathSciNet review: 3326043
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A contact hypersurface in a Kähler manifold is a real hypersurface for which the induced almost contact metric structure determines a contact structure. We carry out a systematic study of contact hypersurfaces in Kähler manifolds. We then apply these general results to obtain classifications of contact hypersurfaces with constant mean curvature in the complex quadric $ Q^n = SO_{n+2}/SO_nSO_2$ and its noncompact dual space $ Q^{n*} = SO^o_{n,2}/SO_nSO_2$ for $ n \geq 3$.

References [Enhancements On Off] (What's this?)

  • [1] Werner Ballmann, Lectures on Kähler manifolds, ESI Lectures in Mathematics and Physics, European Mathematical Society (EMS), Zürich, 2006. MR 2243012 (2007e:32026)
  • [2] Jürgen Berndt, Sergio Console, and Carlos Olmos, Submanifolds and holonomy, Chapman & Hall/CRC Research Notes in Mathematics, vol. 434, Chapman & Hall/CRC, Boca Raton, FL, 2003. MR 1990032 (2004e:53073)
  • [3] Jurgen Berndt and Young Jin Suh, Real hypersurfaces with isometric Reeb flow in complex quadrics, Internat. J. Math. 24 (2013), no. 7, 1350050, 18. MR 3084731,
  • [4] Bang-yen Chen and Tadashi Nagano, Totally geodesic submanifolds of symmetric spaces. I, Duke Math. J. 44 (1977), no. 4, 745-755. MR 0458340 (56 #16543)
  • [5] Sebastian Klein, Totally geodesic submanifolds of the complex quadric, Differential Geom. Appl. 26 (2008), no. 1, 79-96. MR 2393975 (2009b:53084),
  • [6] Masafumi Okumura, Contact hypersurfaces in certain Kaehlerian manifolds, Tôhoku Math. J. (2) 18 (1966), 74-102. MR 0202096 (34 #1970)
  • [7] Brian Smyth, Differential geometry of complex hypersurfaces, Ann. of Math. (2) 85 (1967), 246-266. MR 0206881 (34 #6697)
  • [8] Micheal H. Vernon, Contact hypersurfaces of a complex hyperbolic space, Tohoku Math. J. (2) 39 (1987), no. 2, 215-222. MR 887937 (88d:53033),

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53D10, 53C40, 53C55

Retrieve articles in all journals with MSC (2010): 53D10, 53C40, 53C55

Additional Information

Jürgen Berndt
Affiliation: Department of Mathematics, King’s College London, London WC2R 2LS, United Kingdom

Young Jin Suh
Affiliation: Department of Mathematics, Kyungpook National University, Taegu 702-701, South Korea

Keywords: Contact hypersurfaces, constant mean curvature, normal Jacobi operator, complex quadric, noncompact dual of complex quadric
Received by editor(s): October 12, 2013
Received by editor(s) in revised form: November 23, 2013
Published electronically: February 16, 2015
Additional Notes: This work was supported by grant Proj. No. NRF-2011-220-1-C00002 from the National Research Foundation of Korea
The second author was supported by grant Proj. NRF-2012-R1A2A2A-01043023.
Communicated by: Lei Ni
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society