• Title, Summary, Keyword: contact three CR-submanifold

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SCALAR CURVATURE OF CONTACT THREE CR-SUBMANIFOLDS IN A UNIT (4m + 3)-SPHERE

  • Kim, Hyang-Sook;Pak, Jin-Suk
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.3
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    • pp.585-600
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    • 2011
  • In this paper we derive an integral formula on an (n + 3)-dimensional, compact, minimal contact three CR-submanifold M of (p-1) contact three CR-dimension immersed in a unit (4m+3)-sphere $S^{4m+3}$. Using this integral formula, we give a sufficient condition concerning the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.

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

  • Kim, Hyang-Sook;Kim, Young-Mi;Kwon, Jung-Hwan;Pak, Jin-Suk
    • Journal of the Korean Mathematical Society
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    • v.44 no.2
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    • pp.373-391
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    • 2007
  • 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 $r^{2}_{1}+r^{2}_{2}=1$.

ON CONTACT THREE CR SUBMANIFOLDS OF A (4m + 3)-DIMENSIONAL UNIT SPHERE

  • Kwon, Jung-Hwan;Pak, Jin--Suk
    • Communications of the Korean Mathematical Society
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    • v.13 no.3
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    • pp.561-577
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    • 1998
  • We study (n+3)-dimensional contact three CR submanifolds of a Riemannian manifold with Sasakian three structure and investigate some characterizations of $S^{4r+3}$(a) $\times$ $S^{4s+3}$(b) ($a^2$$b^2$=1, 4(r + s) = n - 3) as a contact three CR sub manifold of a (4m+3)-dimensional unit sphere.

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