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

  • Imsoon Jeong,
    Department of Mathematics, Kyungpook National University, Taegu, 702-701, KOREA
  • Seonhui Kim,
    Department of Mathematics, Kyungpook National University, Taegu, 702-701, KOREA
  • Young Jin Suh,
    Department of Mathematics, Kyungpook National University, Taegu, 702-701, KOREA
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Abstract

In this paper we give a characterization of a real hypersurface of Type~$(A)$ in complex two-plane Grassmannians ${ { {G_2({\mathbb C}^{m+2})} } }$, which means a tube over a totally geodesic $G_{2}(\mathbb C^{m+1})$ in ${G_2({\mathbb C}^{m+2})}$, by the Reeb parallel structure Jacobi operator ${\nabla}_{\xi}R_{\xi}=0$.
Keywords: real hypersurfaces, complex two-plane Grassmannians, Hopf hypersurface, Reeb parallel, structure Jacobi operator real hypersurfaces, complex two-plane Grassmannians, Hopf hypersurface, Reeb parallel, structure Jacobi operator
MSC Classifications: 53C40, 53C15 show english descriptions Global submanifolds [See also 53B25]
General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C40 - Global submanifolds [See also 53B25]
53C15 - General geometric structures on manifolds (almost complex, almost product structures, etc.)
 

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