Semi-parallel symmetric operators for Hopf hypersurfaces in complex two-plane Grassmannians

preprint2014arXivOpen access

In this paper, we introduce new notions of semi-parallel shape operators and structure Jacobi operators in complex two-plane Grassmannians $G_2({\mathbb C}^{m+2})$ . By using such a semi-parallel condition, we give a complete classification of Hopf hypersurfaces in $G_2({\mathbb C}^{m+2})$ .

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Semi-parallel symmetric operators for Hopf hypersurfaces in complex two-plane Grassmannians

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