On some contact CR-submanifolds of an odd-dimensional unit sphere (Q2709945)

The authors consider some natural Sasakian structure \((\varphi, \xi,\eta, g)\) on the unit sphere \(S^{2m+1}\) in \(\mathbb{C}^{m+1}\). They study an \((n +1)\)-dimensional submanifold \(M\) tangent to the structure vector field \(\xi\) of \(S^{2m+1}\) and for any point \(x\) the \(\varphi\)-invariant subspace \(\varphi T_x M \cap T_xM\) of the tangent space \(T_xM\) of \(M\) at \(x\) is denoted by \(D_x\). To determine all submanifolds \(M\) such that \(\dim D_x=n-1\) is the main result of the paper.