Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CONTACT THREE CR-SUBMANIFOLDS OF A (4m + 3)-DIMENSIONAL UNIT SPHERE

  • Kim, Hyang-Sook (Department of Computational Mathematics School of Computer Aided Science and Institute of Mathematical Sciences Inje University) ;
  • Kim, Young-Mi (Department of Mathematics Silla University) ;
  • Kwon, Jung-Hwan (Department of Mathematics Education Daegu University) ;
  • Pak, Jin-Suk (Department of Mathematics Education Kyungpook National University)
  • Published : 2007.03.31
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Abstract

We study an (n+3)($n\;{\geq}\;7-dimensional$ real submanifold of a (4m+3)-unit sphere $S^{4m+3}$ with Sasakian 3-structure induced from the canonical quaternionic $K\"{a}hler$ structure of quaternionic (m+1)-number space $Q^{m+1}$, and especially determine contact three CR-submanifolds with (p-1) contact three CR-dimension under the equality conditions given in (4.1), where p = 4m - n denotes the codimension of the submanifold. Also we provide necessary conditions concerning sectional curvature in order that a compact contact three CR-submanifold of (p-1) contact three CR-dimension in $S^{4m+3}$ is the model space $S^{4n_1+3}(r_1){\times}S^{4n_2+3}(r_2)$ for some portion $(n_1,\;n_2)$ of (n-3)/4 and some $r_1,\;r_2$ with $r^{2}_{1}+r^{2}_{2}=1$.

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References

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