On minimal generic submanifolds immersed in \(S^{2m+1}\) (Q2773271)

The author proved the following theorem. Let \(M\) be an \((n+1)\)-dimensional compact minimal generic submanifold of \(S^{2m+1}\) with standard Sasakian structure \((\varphi,\xi,\eta,g)\) and flat normal connection. If the sectional curvature \(K\) of \(M\) satisfies \(K_{ts}+3g (Pe_t,e_s)^2\geq\frac 1n\), where \(P\) is defined by \(\varphi X= PX+FX\), \(PX\) and \(FX\) being the tangential and normal parts of \(\varphi X\), then \(M\) is a hypersurface of \(S^{m+1}\) and \(M\) is congruent to \(S^{2m-1} (r_1)\times S^1(r_2)\) where \(r_1=\sqrt{\frac{2m-1} {m}}\), \(r_2= \sqrt{ \frac{1} {2m}}\).