Real Hypersurfaces in Complex Two-Plane Grassmannians with Reeb Parallel Structure Jacobi Operator

Jeong, Imsoon ; Kim, Seonhui ; Suh, Young Jin

Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 821-833

Résumé

In this paper we give a characterization of a real hypersurface of Type $\left( A \right)$ in complex two-plane Grassmannians ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$ , which means a tube over a totally geodesic ${{G}_{2}}\left( {{\mathbb{C}}^{m+1}} \right)$ in ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$ , by means of the Reeb parallel structure Jacobi operator ${{\nabla }_{\xi }}{{R}_{\xi }}\,=\,0$ .

Détail

DOI : 10.4153/CMB-2013-018-3

Mots-clés : 53C40, 53C15, real hypersurfaces, complex two-plane Grassmannians, Hopf hypersurface, Reeb parallel, structure Jacobi operator

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