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

• Published in: Journal of the Korean Mathematical Society Vol. 44; no. 2; pp. 373 - 391
• Main Authors: Kim, Hyang-Sook, Kim, Young-Mi, Kwon, Jung-Hwan, Pak, Jin-Suk
• Format: Journal Article
• Language: Korean
• Published: 대한수학회 01.03.2007
• Subjects: 수학; Sasakian 3-structure; contact three CR-submanifold; contact three CR-dimension
• ISSN: 0304-9914; 2234-3008

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 $r^{2}_{1}+r^{2}_{2}=1$.