Abstract
In this paper we study (n + 1)-dimensional compact contact CR-submanifolds of (n - 1) contact CR-dimension immersed in an odd-dimensional unit sphere <TEX>$S^{2m+1}$</TEX>. Especially we provide necessary conditions in order for such a sub manifold to be the generalized Clifford surface <TEX>$$S^{2n_1+1}(((2n_1+1)/(n+1))^{\frac{1}{2}})\;{\times}\;S^{2n_2+1}(((2n_2+1)/(n+1)^{\frac{1}{2}})$$</TEX> for some portion (n1, n2) of (n - 1)/2 in terms with sectional curvature.
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