Remarks on an inequality involving the normal scalar curvature
  We study a pointwise inequality for submanifolds in real space forms involving the scalar curvature, the normal scalar curvature and the mean curvature. We translate it into an algebraic problem, allowing us to prove a slightly weaker version of it. We also prove the conjecture for certain types of submanifolds of $\mathbb C^n$. 
Franki Dillen, Johan Fastenakels, Joeri Van der Veken