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

We study an (n + 3) (n >= 7)-dimensional real submanifold of a (4m + 3)-unit sphere S4m+3 with Sasakian 3-structure induced from the canonical quaternionic Kahler 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(4)m(3) is the model space S4n1+3(r(1)) x S4n2+3(r(2)) for some portion (n(1), n(2)) of (n - 3)/4 and Some r(1), r(2) with r(1)(2) + r(2)(2) (= 1).