• Title/Summary/Keyword: geodesic Reeb flow

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HOPF HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH LIE PARALLEL NORMAL JACOBI OPERATOR

  • Jeong, Im-Soon;Lee, Hyun-Jin;Suh, Young-Jin
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.2
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    • pp.427-444
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    • 2011
  • In this paper we give some non-existence theorems for Hopf hypersurfaces in the complex two-plane Grassmannian $G_2(\mathbb{C}^{m+2})$ with Lie parallel normal Jacobi operator $\bar{R}_N$ and totally geodesic D and $D^{\bot}$ components of the Reeb flow.

COMMUTING STRUCTURE JACOBI OPERATOR FOR HOPF HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS

  • Jeong, Im-Soon;Suh, Young-Jin;Yang, Hae-Young
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.3
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    • pp.447-461
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    • 2009
  • In this paper we give a non-existence theorem for Hopf real hypersurfaces in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$ satisfying the condition that the structure Jacobi operator $R_{\xi}$ commutes with the 3-structure tensors ${\phi}_i$, i = 1, 2, 3.

GENERALIZED KILLING STRUCTURE JACOBI OPERATOR FOR REAL HYPERSURFACES IN COMPLEX HYPERBOLIC TWO-PLANE GRASSMANNIANS

  • Lee, Hyunjin;Suh, Young Jin;Woo, Changhwa
    • Journal of the Korean Mathematical Society
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    • v.59 no.2
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    • pp.255-278
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    • 2022
  • In this paper, first we introduce a new notion of generalized Killing structure Jacobi operator for a real hypersurface M in complex hyperbolic two-plane Grassmannians SU2,m/S (U2·Um). Next we prove that there does not exist a Hopf real hypersurface in complex hyperbolic two-plane Grassmannians SU2,m/S (U2·Um) with generalized Killing structure Jacobi operator.