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Real hypersurfaces in complex two-plane Grassmannians with \(\mathfrak F\)-parallel normal Jacobi operator. (English) Zbl 1260.53093
Romero Sarabia, Alfonso (ed.) et al., Florentino García Santos: In memoriam. Granada: Editorial Universidad de Granada (ISBN 978-84-338-5347-9/pbk). Homenajes, 95-105 (2011).
Summary: We give a non-existence theorem for Hopf hypersurfaces \(M\) in complex two-plane Grassmannians \(G_2(\mathbb{C}^{m+2})\) whose normal Jacobi operator \(\overline R_N\) is parallel on the distribution \({\mathfrak F}\) defined by \({\mathfrak F}=[\xi]\cup{\mathfrak D}^\perp\), where \([\xi]= \text{Span}\{\xi\}\), \({\mathfrak D}^\perp= \text{Span}\{\xi_1,\xi_2, \xi_3\}\) and \(T_xM={\mathfrak D}\oplus{\mathfrak D}^\perp\), \(x\in M\).
For the entire collection see [Zbl 1243.00023].
MSC:
53C40 Global submanifolds
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