Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Real Hypersurfaces in Complex Two-plane Grassmannians with F-parallel Normal Jacobi Operator

  • Jeong, Im-Soon (Kyungpook National University, Department of Mathematics) ;
  • Suh, Young-Jin (Kyungpook National University, Department of Mathematics)
  • Received : 2011.02.01
  • Accepted : 2011.09.14
  • Published : 2011.11.23
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Abstract

In this paper 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 $\bar{R}_N$ is parallel on the distribution F defined by $F=[{\xi}]{\cup}D^{\bot}$, where [${\xi}$] = Span{${\xi}$}, $D^{\bot}$ = Span {${\xi}_1$, ${\xi}_2$, ${\xi}_3$} and $T_xM=D{\oplus}D^{\bot}$, $x{\in}M$.

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Acknowledgement

Supported by : National Research Foundation of Korea

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