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Hopf Hypersurfaces in Complex Grassmannians of Rank Two

Research paper by Ruenn-Huah Lee, Tee-How Loo

Indexed on: 07 Sep '16Published on: 07 Sep '16Published in: Results in Mathematics



Abstract

In this paper, we study real hypersurfaces in complex Grassmannians of rank two. First, the nonexistence of mixed foliate real hypersurfaces is proven. With this result, we show that for Hopf hypersurfaces in complex Grassmannians of rank two, the Reeb principal curvature is constant along integral curves of the Reeb vector field. As a result the classification of contact real hypersurfaces is obtained. We also introduce the notion of q-umbilical real hypersurfaces in complex Grassmannians of rank two and obtain a classification of such real hypersurfaces.