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REAL HYPERSURFACES OF TYPE B IN COMPLEX TWO-PLANE GRASSMANNIANS RELATED TO THE REEB VECTOR

Lee, Hyun-Jin;Suh, Young-Jin

  • Received : 2008.12.11
  • Published : 2010.05.31

Abstract

In this paper we give a new characterization of real hypersurfaces of type B, that is, a tube over a totally geodesic $\mathbb{Q}P^n$ in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$, where m = 2n, with the Reeb vector $\xi$ belonging to the distribution $\mathfrak{D}$, where $\mathfrak{D}$ denotes a subdistribution in the tangent space $T_xM$ such that $T_xM$ = $\mathfrak{D}{\bigoplus}\mathfrak{D}^{\bot}$ for any point $x{\in}M$ and $\mathfrak{D}^{\bot}=Span{\xi_1,\;\xi_2,\;\xi_3}$.

Keywords

complex two-plane Grassmannians;real hypersurfaces of type B;Hopf hypersurface;Reeb vector field;$\mathfrak{D}$-distribution

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