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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
##### Keywords:
normal Jacobi operator; homogeneous hypersurface