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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
DOI: https://doi.org/10.1090/S0002-9939-2015-12421-5
Published electronically: February 16, 2015
MathSciNet review: 3326043
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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$.


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Additional Information

Jürgen Berndt
Affiliation: Department of Mathematics, King’s College London, London WC2R 2LS, United Kingdom
Email: jurgen.berndt@kcl.ac.uk

Young Jin Suh
Affiliation: Department of Mathematics, Kyungpook National University, Taegu 702-701, South Korea
Email: yjsuh@knu.ac.kr

DOI: https://doi.org/10.1090/S0002-9939-2015-12421-5
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