Real hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel shape operator

Imsoon Jeong; Hyunjin Lee; Young Jin Suh

doi:10.2996/kmj/1320935546

Kodai Mathematical Journal

Online ISSN : 1881-5472
Print ISSN : 0386-5991
ISSN-L : 0386-5991

Real hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel shape operator

Imsoon Jeong, Hyunjin Lee, Young Jin Suh

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Keywords: Real hypersurfaces, Complex two-plane Grassmannians, Hopf hypersurface, Generalized Tanaka-Webster connection, Generalized Tanaka-Webster parallel shape operator

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2011 Volume 34 Issue 3 Pages 352-366

DOI https://doi.org/10.2996/kmj/1320935546

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Abstract

We introduce the notion of generalized Tanaka-Webster connection for hypersurfaces in complex two-plane Grassmannians G₂(C^m+2) and give a non-existence theorem for Hopf hypersurfaces in G₂(C^m+2) with parallel shape operator in this connection.

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