Bulletin of the
Korean Mathematical Society BKMS

We study an $(n+1)(n\geq 3)$-dimensional contact $CR$-submanifold of $(n-1)$ contact $CR$-dimension in a $(2m+1)$-unit sphere $S^{2m+1}$, and to determine such submanifolds under conditions concerning the second fundamental form and the induced almost contact structure.

Keywords: odd-dimensional unit sphere, contact $CR$-submanifold, Sasakian structure, almost contact structure

MSC numbers: 53C40, 53C25